Questions regarding del_timer_sync() and re-registering timers

Hi.  The conventional wisdom when mixing del_timer_sync() with timers
that re-register themselves is that the caller must ensure that re-registration
does not happen.

>From kernel/timer.c:
 * Synchronization rules: Callers must prevent restarting of the timer,
 * otherwise this function is meaningless.

Now, the pseudo-code for del_timer_sync and try_to_del_timer_sync looks 
something like this (ignoring the lock manipulation):

while (1) {
        if (timer is not running) {
                if timer is pending then detach it
                break
        }
        else {
                sleep
        }
}

So that the loop continues to spin until the timer function is no longer 
running at which point the kernel checks the pending list and removes it if 
necessary.

Q:  So given this construct, why is it imperative that the timer 
    function not re-register itself?  

I could understand that restriction if the timer function might be running on 
another CPU when the "if timer is pending then detach" step is executed but 
it's not obvious to me how that's possible since base->lock is owned at 
that point (not shown in the pseudocode)?

Can someone briefly point out what I've missed?

Jimmie