The original question you cite refers to code on an Atmel ATMegaAVR - a simple 8 mit microcontroller. In that context, one can assume that the mutex machanism is part of a simple RTOS.
In such a system, there is a thread context and an interrupt context. Interrupts are invoked by the hardware, while threads are scheduler by the RTOS scheduler. Now when an interrupt occurs, any thread will be immediately pre-empted; the interrupt must run to completion and can only be preempted by a higher priority interrupt (where nested interrupts are supported). All pending interrupts will run to completion before the scheduler can run.
Blocking on a mutex (or indeed any blocking kernel object) is a secheduling event. If you were to make any blocking call in an interrupt, the scheduler will never run. In prectice an RTOS would either ignore the blocking call, raise an exception, or enter a terminal error handler.
Some OS's such as SMX, Velocity or even WinCE have somewhat more complex interrupt architectures and support variety of deferred interrupt handler. Deferred interrupt handlers are run-to-completion scheduled from an interrupt but running outside of the interrupt context; the rules for blocking in such handlers may differ, but you would need to refer to the specific OS documentation. Without deferred interrupt handlers, the usual solution is to have a thread wait on a some blocking object such as a semaphore, and have the interrupt itself do little more that cause the object to unblock (such as giving a semaphore for example).
Multi-processor/core and parallel processing systems are another issue altogether, such systems are way beyond the scope of the question where the original comment was made, and beyond my experience - my comment may not apply in such a system, but there are no doubt additional complexities and considerations in any case