I very much agree I cant think of a example that disproves it.
Knowing when your in the ENDGAME MY ANSWER?

you can have a hideaway king and it still be a endgame it just means you'll have a bad or very difficult endgame to play most of the time.

there is a confusion in definition because of theory
In general when there is reduced material on the board and mating attacks against the king are highly unlikely. postitions with Q+ 2pieces of any type has too many middlegame features where a mating attack can occur and decide the game.
Positions where the primary plan to win is now pawn promotion and NOT a mating attack or an attempt to win material then your likely in an endgame (general rule) 2 rooks can generate powerful attacks so this might confound this definition. the reason this is important is once the king is unlikely to come under an attack by multiple pieces it can start to take a more active role in the game.
I would say that 3 pieces on the board is an endgame WHEN queens are not 1 of the pieces.
Endgames come in two flavors
1) concrete endgames that have a clear outcome with best play by both sides. The position is a win, loss or draw, period no discussion needed
2) almost endgames where the above is almost true but not clear (there is a book by Flear that I really like on this subject, he calls them NQE , not quite endgames. the book really shows the thought process strong players go through when looking at positions that can transpose into endgames where things arent 100% clear,...
positions with Middlegame factors can be included in the "not quite endgame" portion, where mating attacks are also a primary consideration.
I think for most amatures and perhaps some masters its hard t truly define when one leaves the middlegame into the endgame. Well I think I've come up with a satisfactory definition of when one enters the endgame in general so here it is. Endgame Phase-When for both sides EXCLUDING the king and pawns both are left with only half or less of the army. When I say half I mean (3 pieces each no matter what the pieces are for ex. Q+2R vs. R+B+N OR Q+R vs 2R+B) and when say less I mean anwhere from 0-3. Well of course this needs critisizm s please comment guys.