This is not true. Different programs on the same system that interoperate and use different versions of the same shared library can absolutely cause issues.

For a trivial change to glibc, it won't cause issues. But there's a lot of shared libraries and lots of different kinds of changes in different kinds of libraries that can happen.

I still haven't nailed if it was due to a shared library update, but just the other day, after running upgrades I was unable to su or sudo / authenticate as a user until after rebooting.