e.g. don’t touch AGPL code unless you also use AGPL

Just to clear this up: copyleft licenses, GPL variants for example, require the license of your code to equally preserve the freedoms provided to your users, or in other words also be a copyleft license. There are some loopholes like GPL on a server, but be very careful when using copyleft code unless you want to use a copyleft license as well.

It gets somewhat murkier when you use someone’s code and base yours on that. IANAL, and that’s very much the legal territory. If at all possible, just reuse the original copyright and license and then derive your work (given the license allows that).

That all depends on the license AFAIK, but IANAL. Most FOSS licenses allow you to do whatever you want while preserving copyright claims, and that includes rewriting or changing the license. GPL forces copyleft, so even if you rewrote it from scratch, you could still be liable if you saw the original code.

For example I've heard that corpos bootleg copyleft code by having completely separate teams doing design and implementation. The implementation team can't ever see any part of the original code, and they have limited communication with the design team. I think that would also go around the copyright claims as well.

If at all possible, just reuse the original copyright and license and then derive your work (given the license allows that).

Or just slap a GPL and subsume everything within a vortex of FREEDOM, and thusly become a true FOSS dude