Breath, and those interested, those possible worthy of special gifts, capable to take,
assuming that accurate is meant in regard of the followed question that might be rephrased "Does the Buddha say here: Giving does not lead to merits, when saying: 'If one were to develop even for just a finger-snap the perception of inconstancy, that would be more fruitful than the gift, the great gift, that Velāma the brahman gave, and [in addition to that] if one were to feed one person...'.
Actually this Sutta (or better wrong understandig of it) is in fact for most wester and modern people the reason why they deny that making merits, developing goodness, is needed and so deny the developing of generosity, sila, if even, without goodness cause of letting go for the sake of beyond.
Most western, moder "Buddhist" are actually training in line of th Jains who seek refuge in what is called householder-equanimity by the Buddha, meaning that they develope ignorance in the cloth of equanimity the construct around the actual path of letting go and factually do not give anything but merely amass in this way. Make simply sacrifies to keep the flame of death alive, loka-dana. See: [Q&A] What happens when your tank is empty, and you’ve got nothing left to give
It's message is also (and with the same cause) that giving without virtue "regardless of whether a gift is coarse or refined, if it is given inattentively, disrespectfully, not with one's own hand, as if throwing it away, with the view that nothing will come of it", or an object of virtue (without reflecting and keeping "buddha, Dhamma, Sangha", un-deluded in mind, has not much value for the path.
Giving so, no good perception of something worthy for gifts (because there is no worthy known or traced), the gift, sacrify is for like-alike, sacrify for like-alike or even lower, leads one there, keeps one there, simply for the sake of keeping the flame of death alive.
Like many (Brahmans, some even for what they think that it leads them to become Buddhas, being Velama, yet not even have wealth to share, to possible differents to Vemala) here. They possible think that they make merits why carring about an "unclean" place, are attached to like-alike and not directing their sacrifies to the three juwels, the Sangha as the unexcelt field of merits. So they nurish just whe world, what ever one nurishes will grow (inwardl and outwardly), and that counts for staring as well.
Doing "merits" in such a way, it is clear that people putting effort into perceptions which are not worthy of special sacrifies, actually just sacrify for their own sake, becoming and selfish purpose.
That is why one should keep right joy in giving in mind, using the three juwels as persection, Nibbana and what leads there, as object of ones deeds, one who seeks for gaining merits, goodness, that leads upwards and beyound. It such is done in an enviroment that does not provide for developing such, has not the purpose for such, is not supported by proper joy, people directed to Nibbana, but simply fot the worlds and becoming sake, to keep the flame of becoming, death alive, its of no fruits of no merits at all:
"Householder, regardless of whether a gift is coarse or refined, if it is given inattentively, disrespectfully, not with one's own hand, as if throwing it away, with the view that nothing will come of it: Wherever the result of that gift comes to fruition, one's mind will not incline to the enjoyment of splendid food, will not incline to the enjoyment of splendid clothing, will not incline to the enjoyment of splendid vehicles, will not incline to the enjoyment of the splendid five strings of sensuality. And one's sons & daughters, slaves, servants, & workers will not listen to one, will not lend ear, will not make their minds attend for the sake of knowledge. Why is that? Because that is the result of inattentive actions."
Is like in MN96:
“Brahmin, it is like a poor miserable man against his wish was told, here good man, you should eat meat and you should not spend money on it. In a likewise manner, without the consent of recluses and Brahmins, have appointed these four services. Brahmin, I do not say all services should be done. I do not say, all services should not be done. When doing those services if there is evil, that service is not good. I say it should not be done. When doing those services, if there is no evil, that service is good. (and vici vera).
Like the person who had put Sister Uppalavannas translation with a lot of sacrifies on the web (obove linked), he had possible made it in a manner of no fruits to aspected from it, althought it might come to frutaions. Possible without keeping Silas, respectless, thinking on amasing for ones own sake or what holding as self/real. Doning for reputations, wealth (physical, mental by knowledge), praise, pleasant feeling... invest his sacrifies for unreal and not to real directed sakes. Not to tend up-wards, most not even tend as it currently is, up simply wasts his als goodness, merits away.
Many of modern lay or opposing undertakings and practices, and their ways, unguided, self-over-estmating in wealth and possiblities, simple waste old merits an goodness possible earlier attained. So it is with all that meditation stuff and well-ness-buddhism, all simple certain ego or not-ego trips.
Be attentive, pay proper attention and learn to judge more wisely, step by step, with real benefical sacrifies and their targets!
[Later Addition (on account of an answer here) to understand quality of Dana better:
There are 3 factors:
The giver (his mindstate, directed to...? free of moha, lobha, dosa, or not) - since Velama was an "ordinary" being, perfection can not be aspected, he also had neither inwardly nor outwardly an access to the tripple gems or the/a Buddha, could possible not even images such.
The recipient (since at this time there where no Buddha no Sangha and the gifts might not have been given to a Pacceccabuddha, they have been directed to "ordinary" people.)
The gift (it was clearly outstanding and therefore had it's certain frutation)
The Suttas give direct 6 factors: Dana Sutta: Giving
When one has the wrong perception of a worthy recipient, holding something not really worthy for worthy, thinking this or that wordling is a Noble one, having no perception of those following the Noble One, it is to be assumed that the gifts are given out of right view and so have not much value in direction of Nibbana. People think normal not in spheres of free of fetters but on what ever benefits or wordily aims. Having the tripple Gems possible still present, many are gifted with that unexcelt field of merits and it is merely "sad" if not used.
That is why just a spoon of rice, with the right mindstate to a worthy person excells even the biggest wealth given if this two factors are not perfect. Or just the Veneration torward a Noble is many times higher as doing charity to torward ordinary people day by day, the whole year. See dhp]
More on Dana, note that the princip in it counts also for the merits sila, samadhi, can be found with references and discussion here: Dana (Generosity, Charity) "Abhidhamma in daily life "
May this sacrify made by me, benefit those able to rejoice with it, lead to highest bliss, path and fruit, and may the Devas inform those who do not have seen or heard yet.
A possible extended answer as well as space for questions and discussiin can be found here.
[Note: This is a gift of Dhamma, and not meant for commercial purpose or other gains in this world.]