Table Doesn't Tell Officials That the Player Fouled Out

[johnnyrao]

Originally Posted by Nevadaref

It happens. As evidenced here.
Names redacted in the following situation:

3-pointer from the top of the key made it a 71-66 game with 2:39 to play. But the [Xs] watched as the [Ys] struck for five straight points in a 30-second span, four by [Y1] and a free throw by [Y2], tying the game at 71-71 with 2:01 on the clock.

[X1] hit a pair of free throws as part of his 14-point fourth quarter, but [Y2] and [Y1] answered right back with back-to-back buckets, finally giving [Team Y] the lead at 75-73 with just over a minute left in the game.

Ironically, the [Ys] should never have owned the lead. [Y1] re-entered the game with 3:02 remaining, but he had committed his fifth foul earlier in the fourth. It wasn't until he picked up his sixth foul that the officials claimed responsibility for the mistake and did not punish [Team Y], so [Y1]'s six points during the 9-2 run remained a key factor.

What would lead the officials to think they made a mistake here? I am guessing that when he was assessed his fifth foul earlier in the quarter, the improper procedure was used and the coach and player were not notified? If Y1 fouled out and the coach/player were properly notified, then couldn't the officials assess that the Y Coach was unsportsmanlike by re-entering Y1, knowing he had already committed 5 fouls? I'm confused on this one and would ask for clarification.