So far, we've covered the production explanation (none known) and could sum up the canon explanation quickly enough, too (none given).
That leaves the question of the in-universe explanation. Star Trek didn't change
so radically that the early episodes would have to be accepted as describing a completely different set of heroes. Yet it's quite possible that the heroes went from serving one organization to serving another. Did the
Enterprise sail under two different colors in the late 2260s?
Well, literally speaking, we did see two flags being flown in the briefing room...
On two occasions, Kirk brings up the United Earth Space Probe Agency, making it look as if this organization took Starfleet's place in two episodes. In the spinoff shows, UESPA remains an "in-joke" to be inserted in off-focus graphics and the like - until ENT shows us that UESPA existed in parallel with the United Earth Starfleet, sharing heraldic space in a symbol decorating the floor of a meeting room at Starfleet Command, San Francisco.
http://ent.trekcore.com/gallery/albums/4x20/demons_021.jpg
Does the symbol refer to a joint operation between two organizations? Or a hierarchy of organizations? In either case, and assuming that the UFP Starfleet inherited the position of the UE Starfleet here, Kirk might vacillate between telling people that his employer was UESPA or that his employer was Starfleet.
If it's a hierarchy, we could well assume that UE is the lower level and UFP the higher, and that Kirk is being overtly local in considering himself an Earth rep. If it's a joint operation, tho, Kirk might at times be doing scientific missions for a "Space Probe Agency" just like the US Navy might help out NOAA in meteorologic work, or provide Antarctic expedition support.
The latter interpretation has some supporting evidence, if we choose to read it like that. In "Corbomite", Kirk is doing starmaps. In "Tomorrow is Yesterday", his ship has been fooling around with a black star for no obvious reason. In "Charlie X", UESPA is the organization in charge of a transport vessel that for some mysterious reason surveyed a rarely visited planet. Quite possibly a NOAA analogy, then.
Timo Saloniemi