I don't know. The whole thing just kind of feels like it was originally copied from the comic, but then someone didn't think an origin that relied on three people getting murdered was OK for kids, so it was just sloppily altered.
I mean the basic beats of the comic origin goes like this:
- Yoshi flees Japan after he murders Nagi.
- Shen and Yoshi are murdered by Saki, so Splinter (the rat) goes down the sewer.
- Splinter mutates by touching the ooze covered turtles, which turns all of them into humanoids.
And in the FW show it goes like this:
- Yoshi flees Japan after he's accused of a murder attempt.
- He (an educated human being) goes down the sewer.
- Yoshi mutates by touching the ooze covered turtles, which results in them mutating into identical humanoids while he becomes a rat.
You can sort of tell by how sloppy it is, it was probably going to be the original origin before a re-write.
Edit: And I've said this before, trying to explain how the same localised incident causes four identical transformations and one extremely different one is just jumping through pointless hoops.