I think you are way overanalyzing this. If we complete one additional pass then we are in field goal range with a chance for points. On many 4th downs we will punt, because it will make it harder for the other team to score. With such little time left, there is a very slim chance of Purdue scoring because we are trying to get points before half.
It is irrelevant if Meyer thinks they will be able to scheme over half time and put up more points later. When you have the ball and a chance to score, you are going to take it. Urban makes each decision based on what he thinks is right to do at the time. To me, going for points was low risk/high reward. Apparently you deem this low risk to be too high. You have a right to do that, but I have no problem with Urban's decision. In fact, you would probably have heard some boos from the crowd if Urban played it safe, as they would have deemed the risk worth the potential reward. Would they be right? I don't know, but I personally have no problem with it.
If you want to argue what is necessary, I could argue that there is no point in even putting Braxton into the game until we fall behind. Just put Kenny in and try to run the ball with Hyde to see if we can win on that alone. If not, then heck, there is still more time for us to change scheme and win the game. That way we minimize risk of injury to Brax and still leave ourselves the opportunity to win the game. It's the same idea as letting a possession before half go (a possession where you are not backed up and at high risk for giving up points). It's not strictly necessary, so why risk it?
I'm not sure what the example with the fumble has to do with this situation. You are arguing game management, not player fundamentals. Perhaps you are arguing safe vs. going for points? Well falling on the ball gives your offense a chance to score points, while going for the scoop is trying to score now. Taking a knee is not the same. You don't gain a possession by taking a knee, you are going to get that even if you go for points. A more fitting situation would be following a blocked punt. Players are taught to NEVER fall on a blocked punt, and to always scoop and score. That is because even if you don't get the ball, you are given the ball on downs anyway, so you might as well try for the score. Similarly, we were getting the ball in the 2nd half anyway, so why not go for the points?