People might wonder why. Since these statements sound incompatible.

The GPL requires two things, mainly, if you're going to use something GPL in a closed source package.

1) Attribution. You can't just take and not comment.

2) Modifications should be made available under the same license.

this means that if you're using GPL software and including it as a shared object, then you're fine.

If you need to modify that software to make it work for you (including fixing bugs) then you need to make those elements available.

This is different than insisting that anything that touches GPL code be GPL also.

Some proprietary licenses do have provisions for this, which makes them GPL incompatible.

This seems very misleading. A library released under the GPL cannot be used by non-GPL software. That's by design. It's the reason for the more permissive LGPL licence.

edit For brevity I ignored dual licensing. If you release your library under both GPL and Apache, then things are of course different.

https://www.gnu.org/licenses/why-not-lgpl.en.html

I thought that was the LGPL, but the GPL requires anything using it (as an include, not a standalone binary) to be GPL as well.