"Learning it from a book"

[neatoman]

So while becoming martial arts master from a book is kinda dumb it's not as offensive in retrospect, the most offensive aspect isn't so much that Splinter did it but rather that he did because he thought it was a good parenting guide. Sure, a book alone isn't going to make a master but it's at least going to get you started on the basics, that's what an educational book is for.

Alone this explaination for "How does a rat know martial arts?" isn't very satisfying, but I think it could be combined with the original explaination to justify the perceived flaw of "Rats can't learn from seeing someone train!". I think "He saw Hamato Yoshi train, then supplemented that with teachning tools like books", might be the the most satisfying compromise between keeping the original origin and alleviating the questionable logic.

That way you don't have introduce reincarnation if you don't like it, nor do have to jump through hoops explaining how the same exact event caused a man to transform into a rat and turtles into humanoids.