Does mainstream Buddhism agree with the above?
Yes I think so.
I don't know any DBT except what you quoted, so by "the above" I assume you mean the first quote, about "negative emotions" and "finger-trap".
The "negative emotions" are a subject of Buddhism, see e.g. Kleshas (Buddhism) where they're translated as "Afflictive emotions". The different schools enumerate them differently (depending on how you analyse them there may be 2, 3, 6, or 50 of them), but I think that all schools agree they exist and are a problem.
Some schools might suggest there's only one way to solve the problem -- i.e. "the Noble Eightfold Path" (which is the fourth of the "Four Noble Truths") -- or perhaps all schools agree with that.
I think that user13190's answer is a summary or paraphrase of the Dhammacakkappavattana Sutta.
Even so, different schools have different practices and so on.
When you get into details of how to solve the problem, what the solution is, I suspect that Buddhism probably differs from DBT -- otherwise wouldn't DBT be Buddhism, indistinguishable?
Assuming you may find the Dhammacakkappavattana Sutta difficult, another popular snippet might be this from the Dhammapada:
"He abused me, he struck me, he overpowered me, he robbed me." Those who harbor such thoughts do not still their hatred.
"He abused me, he struck me, he overpowered me, he robbed me." Those who do not harbor such thoughts still their hatred.
Hatred is never appeased by hatred in this world. By non-hatred alone is hatred appeased. This is a law eternal.
I think that (i.e. whether an afflictive emotion like "hatred" is "stilled" or not) is reminiscent of the "finger-trap" you mentioned.
The first two verses:
Mind precedes all mental states. Mind is their chief; they are all mind-wrought. If with an impure mind a person speaks or acts suffering follows him like the wheel that follows the foot of the ox.
Mind precedes all mental states. Mind is their chief; they are all mind-wrought. If with a pure mind a person speaks or acts happiness follows him like his never-departing shadow.
... imply that the mind (e.g. it whether it harbors or doesn't harbor such thoughts) conditions (creates conditions for, is followed by) suffering or happiness -- maybe (I don't know, but I guess) DBT says something along those lines.
Oh -- the title of what you quoted, "acceptance and change", sound a bit like Buddhist doctrine too -- Buddhism teaches that things are impermanent (change), and I think it teaches (e.g. in the second of the four noble truths) that being attached to things is a cause of suffering -- see also for example Why do the Noble Truths talk about 'craving', instead of about 'attachment'?
Buddhism is kind of complicated though; people might resist it for various reasons, including the one you mentioned -- or for an opposite reason, e.g. that people don't want to see "suffering".
Also I might have given have an opposite reply, and said that everything is suffering (or is, at least, unsatisfactory) -- sabbe sankhara dukkha -- that too is hard to explain, and even that is a topic which different schools of Buddhism may summarise differently, see e.g. Differences between the tilakkhana and the Dhamma seal
It's not clear what you mean by "pain" in the question.
I assume that maybe you don't mean physical pain -- see e.g. Experiencing physical pain -- so maybe you mean something metaphorical.
In that case you'd asking whether there's a difference between "metaphorical pain" and "suffering", which I think is quite vague.
The Pali word that's translated as "suffering" is Dukkha (maybe we should define the dukkha and suffering tags to be synonyms).
And actually dukkha doesn't mean exactly the same as suffering (so much so that people prefer to refer to it as "dukkha" instead of as "suffering"), so that's another way in which the question is inherently imprecise.
Reading the quote "... a type of psychotherapy that combines behavioral science with Buddhist concepts like acceptance and mindfulness" reminds that I have had one second-hand (i.e. hearsay) experience of a DBT practitioner: which was, as a treatment for PTSD (the trauma of having been assaulted), being advised to be "mindful" of the present environment.
For example, when you're taking a shower, instead of having "flashbacks" (i.e. reliving the experience of being assaulted), to "remember" where you are at the moment, e.g. in the shower, feeling the touch of water, hearing the sound of water, and so on.
That is not unlike some practice Buddhist practices, where "mindfulness" is a meditation and or part of the doctrine -- see e.g. What does sati mean? but see also Where is the suttas is 'sati' defined as present moment awareness?