I know almost nothing about Android app development and especially disassembly (if that's even the correct term): Is it possible to modify an apk to eliminate this flag anywhere it's set?

I assume in the case of apps trying to protect copyrighted content, the answer is likely "yes but the app might check its own signature and exit if it's not valid, which it won't be at that point, so you'd also need to rip that out, which makes the job way harder."