Why?

Just because you're not on duty, that doesn't mean you are at rest. The opposite is also true. Just because you're not at rest, that doesn't mean you are on duty.

Travel not local in nature is one where you're neither on duty nor at rest. Same with "on call". You're neither on duty nor at rest.

There's no contradiction. Just a flaw in the way you want to interpret them.

Remember that for 135, the FAA cares only about rest. "Have you had your required rest?" Not "have you been off duty long enough?".

-mini