Does the granting of a request to route from A to B at level C amount to a transit of controlled airspace on that route?
For obvious reasons, that is not a question that can be answered without knowing the precise phraseology used on both sides of the conversation.
Generally speaking though, a pilot is required to know and understand whether or not he can legally execute an instruction or clearance. That is not the ATCO's responsibility. If in doubt, ask.
2D