What you're saying doesn't contradict the argument that the goal was do outdo the black panther lunch programs.

Certainly I'd like to read more about the idea before I buy into it, but it does make a lot of sense - schools in black neighborhoods are chronically underfunded and the black panthers were first and foremost a direct action and mutual aid group, and furthermore the USA government viewed them as a huge threat to government authority and did many things to attempt to undermine the black panthers... Including outright assassination.