Does full nose up trim yield best glide in Cessna 172/152 for a given load?
That ground instructor is giving you bad information. You can not make a blanket statement like "full nose up trim" and expect it to be valid for any and all situations.

You are correct that the best L/D speed will yield the best glide ratio and that the speed will vary with weight.

The best trim position is the one that will maintain the best glide speed hands off. Any other trim position will require an additional control input to fight the trim and that input will cause additional drag.

So no, full nose up trim will not yield the best glide unless by some remarkable coincidence that is also the trim position for hands off best glide speed.