We can, however, rule out "standard mission" because of Kirk's circumstances: he's on Earth, three months from retirement, and has to move back into his quarters and unpack for this insane mission Spock just volunteered him for. Meanhile, Scotty just bought a boat, Uhura's supposed to be doing a seminar at the Academy and Bones is wondering where Sulu is (has either forgotten or is unaware that Sulu is now commanding the Excelsior).
This all suggests the "crew of the Enterprise" haven't been together ON the Enterprise in quite some time, assuming they've even been together at all (McCoy, at least, has not) and have been involved in a whole bunch of other non-starship related things in recent months. Three months from retirement, they are not about to start a brand new deep-space exploration mission and they're certainly not just coming BACK from one.
So I'm thinking that they're not a "crew" at that moment so much as a loose association of senior officers who continue to find themselves in highly influential positions; Kirk and Uhura (and possibly Spock) are still instructors at the Academy, Chekov is either between assignments or getting ready for his next command (First choice for Enterprise-B with Harriman as backup?) Bones is off somewhere being Bones. It's not even certain that they've been together on the Enterprise since the Sha Ka Ree fiasco; considering the anomalously high ranks of the entire bridge crew at this point, it's pretty unlikely that they were.