Srama,
I am saying this is fundamentally OK if you think hard about it.
Why do I have to think hard? What if I am in the rest frame of two
particles interacting (they aren't moving but I need an event). But I
have a mediating particle (photon, W, Z, or gluon - maybe even a
graviton) that has to travel to transmit the information about the
interaction. This is the "lowest form" of motion I can imagine. This
is even below the Fermi motion of the quarks within the nucleon.
However, I would not say that if no motion, no time; but rephrase it as
if no interaction (or exchange of information), no time. Time is
relative after all.