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Different teams often make the same mistake. The system you describe is not perfect, but makes sense.

I neglected to mention there was a third party that reviewed the algorithms to verify they weren't the same.

Nothing is perfect, though, and the pilot is the backup for failure of that system. I.e. turn off the stab trim system.

Is this still the case for simple algorithms?

I don't know as much about modern avionics.

if this is true, then would it be a better investment to have the 2nd team produce a fuzz testing/systematic testing mechanism instead of producing a secondary copy of the same system?

In fact, make it adversarial testing such that this team is rewarded (may be financially) if mistakes or problems are found from the 1st team's program.

Such incentives can lead to reduced collaboration. If I get paid every time you make mistakes, I won't want you to get better at your job

the whole point is that they're not collaborating so as to avoid cross-contamination. also you don't get paid unless and until you identify the mistake. if you decrease the reward over time, there is an additional incentive to not sit on the information

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