When reading the Sophie Charlotte biography and coming to the part where young FW hates his Latin lessons and flute lessons (yes, he had them), not to mention his dance lessons, I sighed, because you can see the "MY CHILDREN WILL NEVER HAVE TO DO THIS" forming in his head, followed by "why is my ungrateful oldest son not full of affection and gratitude to me that I'm sparing him this but wants to do all I hated? He must hate me!". So yes, for all we know, Peter and Fritz were just caught book sharing. (Which would explain why Peter just gets transferred and not punished or threatened with hellfire.)

Here's a thought: what if Sophie Charlotte had lived a few decades longer instead of dying young and in her 30s? It would have caught FW in a bind, because he was so much into respecting your parents, and he couldn't have objected if his mother at her court would have (openly, not in secret) provided Fritz with cultural opportunities.