Yes this can happen, though it should be noted that a nonprofit health insurer would be regulated differently than a nonprofit research institute that isn’t responsible for providing or reimbursing care.

There can be corruption in governments and government programs too — but still the data says they do a better job at optimizing public health than for profit environments. Not letting perfect be the enemy of good, or better, it’s pretty clear from what I can gather that non profit is better than for profit, and optimized single payer is better than both of those.