This was fixed after several attempts in the past [1] and I convinced
myself that I was doing it wrong when I implemented generic VSC rules
similarly to how VTC rules were centralized [2] but some lessons will
never be learned.

The reason why I was so easily convinced is that the '-local' suffix
is clearly documented, but the '-am' one is not, which leads me to
believe that it is an implementation detail we shouldn't rely on. The
documentation clearly states the lack of '-local' ordering, one more
reason not to rely on 'check-local'.

If we can use neither 'check-local' nor 'check-am' reliably for the
test suite refresh vs execution ordering, maybe there's a simpler
solution?

Fixes #3942

[1] 85e3d442
[2] dcaf616c