Hi Lorna! I think "fix twice" actually goes well with "only handle it once" if we're thinking long-term. When a system fails, everyone makes it first priority to get back to the baseline. It's a fire. Drop everything. Stephen Covey would call this quadrant 1 -- important and urgent.
However, once we're back to baseline, there's usually little organizational pressure to do anything more. It takes a special mindset to take the fix further, preventing a future recurrence. This would be quadrant 2 -- important but not urgent.
It's the 2nd fix, preventing a future recurrence, that is most loyal to "only handle it once" because (theoretically) we should never have to return to the issue. That's how I think about it.