Uhura was probably told by Starfleet something like "Well done, guys, now stop creating more crises and retire ASAP", as regarded the top officers of the ship, while nothing was said about the ship. Kirk then assumed the ship would be handed over to new folks. But some time after their return, Kirk learned differently. The decision might have been made as the result of damage assessment done after arrival, long after the end credits had rolled.
The only deadline we have for the decision, really, is that Starfleet needed enough time to paint the new name on the E-B and to send out invitations for VIPs and press for her launch. Perhaps the decision to retire the E-A was made three days before the GEN teaser scene?
Ships are decommissioned. Officers are either cashiered (see General Stanley McChrystal...) or allowed to retire.
I am thinking what Uhura is referring to is that the Ent-A was informed via subspace by the Admiralty that the ship would be decommissioned upon her return to Earth, given (1) a political need to show both the citizens of the Federation an immediate "peace dividend" of the end of a Cold War with the Klingons and demonstrate committment to the peace process with the Klingons [and what better way to demonstrate to them by beginning to decommission what they view as "battle cruisers"?] and (2) the sting of decommissioning Ent-A would be alleviated somewhat by the announcement of giving her name and registry to a new Excelsior-class ship. Additionally, though the ship may not necessarily have been first on the chopping block, the damage she took during the battle with the BoP may have shot her to the top of the list...no sense spending good credits and materials to repair something that's long in the tooth as it is. AND, they might have been formulating plans to turn Ent-A into an exhibit at the Fleet Museum, leaving her battle wounds intact.
Of course, your interpretation might also be correct and Uhura was just being discreet on behalf of the young ears on the bridge. After all, nothing inspires more confidence among the ratings and junior officers on a shot-to-hell ship crippling back to Earth after a pitched battle with the entire peace process at stake than knowing your senior officers are gonna get fired when you get home...given the rather dubious nature of Kirk's "command style" and his, uh, creativity when it comes to following orders, his superiors may have decided post-Khitomer Conference that enough was enough and pulled the plug on the guy before another calamity befell them. Sure, everything worked out just fine in the end, but it could have all easily gone south.
Kirk's comments "This ship and her history" might have been construed to mean the moving of the name and registry to the new Excelsior...or he might have already been plotting some way to keep her around after he was gone, whether to persuade the powers-that-be to give Chekov a shot at the captaincy, or for the events that ultimately led to the Shatnerverse book. How you define the "This ship and her history" line is subjective listening. Something like "Let's eat, Grandma!" versus Let's eat Grandma!"...
Regarding the Yorktown/Ent-A debate, the decommissioning comments do give more credence to that theory, that Ent-A is the old USS Yorktown as damaged by the Whalesong Probe in ST4. And given that the crew may well have died in that incident, the decision-makers might have gone ahead and given Yorktown's name over to a new Excelsior-class; when Kirk and company saved the day, they then decided to "regift" Yorktown and give him the ghost ship to keep him happy. He would have been so giddy to get a ship again that he may not have asked the tougher questions. Kirk gets an Enterprise, an Excelsior-class gets the Yorktown name; everyone's happy and it's a win-win for all parties involved.
(a brief conversation overheard in Transporter Room 1 right before Ent-A leaves SpaceDock for the ST5 mission...
Ensign Redshirt..."Hey, Chief, isn't this ship the old Yorktown? Y'know, the one where the entire crew died horribly in the cold dark of space when the Probe drained all power, even from the lifeboats and EVA suits?"
Old Chief..."Naw, kid; that's just an old fuckin' sea story. Don't worry about it. I'm going on leave now, but have a nice flight to Nimbus 3...and keep an eye out for all-powerful alien entities!")
That also goes a long way to explain the various tech anomalies plaguing Ent-A in ST5; as aftermath from the Probe exposure despite Scotty's best efforts. For all we knew, the Saratoga suffered from the same effects.
I think what the author of "Mr Scott's Guide To The Enterprise" was getting at when he called the new ship the former USS Ti-Ho was that he meant perhaps the former USS Taiho, which was a WW2 Japanese carrier sunk in the Battle of the Philippine Sea. If he's on the BBS somewhere or someone knows where he is, we could ask him.