I think this simple narrative is more legend than fact.
Prohm started with a "normal" lineup and went small pretty early. Young played 20 minutes, Bowie played 13, and Nick played three minutes. Every other minute was played by a guard (assuming Burton counts as one).
Purdue built and held a lead despite that. What changed the game around was hot shooting.
The Iowa State run to go from down 19 to up 2 consisted of...
Naz three
Monté made two free throws
Bowie two
Thomas two
Monté two
Jackson three
Monté three
Monté two
Thomas two (down three)
Burton two
Burton two
Burton three
Burton made two free throws
Thomas two (ties the game)
Burton made two free throws
Burton then, bless his heart, was "feeling it" and... shot the team out of the game. The scoring drought from 3:10 to 0:53 let a two-point lead turn into a three-point deficit, and they could not pull it out.
Iowa State possessions after being up two --
Burton miss
Monté turnover
Naz turnover
Burton two
Monté made two free throws
Monté missed three
Four points on six possessions = 0.67 points per possession... not great.
The deficit had already dropped from 19 to three by the time Burton started to go off, which was certainly helpful, but it wasn't enough to win the game. And often is the case with hot shooting, when it turns cold, things can go very badly for you very quickly, which was what happened the last three minutes of that game.
I think a more reasonable reading of the facts of that game is Purdue started strong, Iowa State made some adjustments to put more guards on the court, but Purdue maintained its lead until Iowa State unleashed hellfire from three (mostly Naz, Monté, and Jackson). But then the hellfire froze over, either from cold shooting or Purdue having made some adjustments back against the shooting-centric lineup, and closed it out after weathering the storm. It sucks, certainly, but I don't see any evidence that an immediate small lineup would have won the game. Indeed, it had its chance.
That same small lineup had a two-point lead with 3:10 left and managed to lose by four.