If we are using the BASEPRI register to disable interrupts, then the answer is that we must disable ONLY the "normal interrupts". That is because we cannot disable SVCALL interrupts and we cannot permit SVCAll interrupts running at a higher priority than the high priority interrupts (otherwise, they will introduce jitter in the high priority interrupt response time.)
Hence, if you need to disable the high priority interrupt, you will have to disable the interrupt either at the peripheral that generates the interrupt or at the NVIC. Disabling global interrupts via the BASEPRI register cannot effect high priority interrupts.
