The problem, in my opinion, is not so much that the Doctor is strongly persuaded that he is as aliving being as any living aboard but that Janeway and her senior crew strengthened him in this opinion, surely because they ended up believing themselves that the Doctor was one of them, while the truth is very different. To believe in something does not make the thing exist insofar (here, the Doctor is "born" as a hologram and mobile ermitter or not, he will "die" as a hologram. His existence will be always linked to a powerful generator and other equipment, which could be switched off at anytime). And as it always did in similar situations, sooner or later, and probably sooner than expected, the reality of his condition/existence will come back to haunt him (and indirectly to his supportive friends), once back to the reality. Earth (or whatever other planet/zone of the Federation) isn't Voyager, the crew isn't a representative a cross-section panel of the popluation living in the Federation. In short, there where his sentienty allows the Doctor to be considered as a full member of the crew (Voyager) and above all, as a "living being", the population of the Federation can still considered him as a common hologram only good to serve them and to obey to their orders, regardless his extended knowledge.
Added to this, I would repeat - as I had already done in the past - that, even IF, assuming that the Federal judge's positive opinion about the procedure of recognition of Holo people's rights was followed by his pers and the law got the agreement of the leader of the Federation, the holograms were freed, The Doctor wouldn't. Indeed, even if his existence is due to an active collaboration between Dr Lewis Zimmerman & Starfleet, the latter will assert his property because he was created in a military purposes (to equip the vessels with an emergency doctor to replace or help the current ship's doctor) and funded by Starfleet. Morever with his new knowledges acquired throughout the 7 years spent on the ship (thanks to Janeway, Harry Kim & B'Elena Torres), he could become a danger for the both organizations (Federation & Starfleet) if he fell into enemy hands or decided to take advantage of his new autonomy (the Doctor showed us how independent and selfish he could be when he wanted). Never Starfleet (and/or the Federation) would risk their security for a hologram - as brillant as he is -, who would enjoy his new freedom and let me say that Janeway, even newly promoted Admiral, could not act in favor of the Doctor because this would go well beyond her responsibility and Starfleet would remind her if necessary.
