Read the cake before you touch the vial. An intact, opaque, evenly distributed puck that sits proud of the vial base is what a good lyophilisation cycle produces. Anything else — collapse, melt-back at the stopper, a glassy film, a cake that has slumped to one side — is evidence about the cycle, the shipping, or both.
On re-freezing something that thawed in transit: if it arrived as a lyophilised solid that warmed but never got wet, re-freezing costs you nothing except the thermal cycle.
In practice, room temperature before drawing is worth the ten minutes. Cold solution is more viscous, draws slower, and is more likely to pull a bubble past the plunger seal.
Coring of elastomeric closures is a well-characterised failure mode in the parenteral packaging literature.
The caveat on all of this is that it assumes the vial contains what the label says.
None of this is exotic. It is just the difference between doing it deliberately and doing it approximately.