Well, you are right for most practical purposes. My formulation is more cautious.
VA of a core is a practical way to express the ability of that core to carry over energy i.e. power. But that may be not the power that is used at the secondary. What if the load on the secondary is purely inductive? No ACTIVE power is used, but the voltage may be high, the current may be great, and the flux in the core must be able to produce these high values at the secondary. Plus, of course, to cover for any losses.
What you call "nominal" is "on a permanent basis" in my formulation. As with most limits, excesses above nominal values may be tolerated if not too large and never for long periods.