The Zen story titled "Is That So?" (I suppose you know it) suggests that it's possible to 'function' as a parent, filling the needs of the child, without especial attachment to that child nor to the role of parent.
If I look at the world (society) then I see many mothers and fathers, sometimes.
Recognizing the bond or relationship between children and parents may be important for the avoidance of suffering (and so denying it is wrong)? The Buddha set a rule for example that people need their parents' permission before ordaining, I'm pretty sure
that's an example of the Buddha's not denying that 'parents exist'.
I'm not sure about the phrase you quoted and perhaps you're misusing it if you use it out of context. I can't presume to know what was meant in context but I read as something like,
There is no "my" mother and father, without "me" (i.e. the self).
Extending the phrase to add "without the self" to every sentence sounds like a word-game (and it seems to me that a lot of recent questions on this site have been based on "logic").
If you're asking what "right view" is, perhaps that's better defined in another sutta than in MN 117 -- i.e. in SN 12.15 -- I'll quote it all because it's quite short, it contains several famous phrases:
Kaccānagotta (SN 12.15)
Then Venerable Kaccānagotta went up to the Buddha, bowed, sat down to one side, and said to him:
“Sir, they speak of this thing called ‘right view’. How is right view defined?”
“Kaccāna, this world mostly relies on the dual notions of existence and non-existence.
But when you truly see the origin of the world with right understanding, you won’t have the notion of non-existence regarding the world. And when you truly see the cessation of the world with right understanding, you won’t have the notion of existence regarding the world.
The world is for the most part shackled by attraction, grasping, and insisting.
But if—when it comes to this attraction, grasping, mental fixation, insistence, and underlying tendency—you don’t get attracted, grasp, and commit to the notion ‘my self’, you’ll have no doubt or uncertainty that what arises is just suffering arising, and what ceases is just suffering ceasing. Your knowledge about this is independent of others.
This is how right view is defined.
‘All exists’: this is one extreme.
‘All does not exist’: this is the second extreme.
Avoiding these two extremes, the Realized One teaches by the middle way:
‘Ignorance is a condition for choices. Choices are a condition for consciousness. … That is how this entire mass of suffering originates.
When ignorance fades away and ceases with nothing left over, choices cease. When choices cease, consciousness ceases. … That is how this entire mass of suffering ceases.’”
This is echoed in the Vajira Sutta (SN 5.10).