Military personnel earn 2.5 days of leave each month (30 days each year). That seems like a lot, but they get charged leave for days that would ordinarily be considered free time -- for example, if you go on a long weekend trip and take Friday and Monday off, you are charged four days of leave. Nevertheless, one of the things the recruiting brochure fails to mention is that you often won't be able to take time off. You're allowed to bank up to 90 days of leave (it was even bumped up to 120 days for several years after 9/11); after that, you lose the leave without compensation for it. It is permissible to take up to 30 days leave in advance, but more than a few day's worth generally only happens for special reasons such as a family emergency. Most people try to keep 10-15 days on the book for such contingencies.
Taking a large chunk of leave requires advance coordination with your command. It helps if they like you, you're a good performer, and have a respectable reason for doing so. Seaman Slacker who wants to go take trapeze lessons is not going to get the same consideration as Lieutenant Commander Competent who agrees to take on extra duty schedules before and after his absence. It still comes down to needs of the Service, and they could have canceled his leave if something else had come up.
Depending on timing, the filming may have been scheduled at the same time that he was transferring between units. It's common for servicemembers to take large periods of leave then because you often don't have specific commitments then. (Though that is still constricted by unit schedules. You can't take 30 days of leave if the ship you're going to is sailing in 20 days.)
It's also possible, though I don't think likely in this case, that he may have been given permissive leave orders (time away that is not charged to personal leave time) to participate in this show as a public affairs gig for the Navy. If he were running around in a Go Navy t-shirt and giving a lot of interview time about his work, I'd be more inclined to think so.
Edited March 26, 2015 by SassenachncG1vNJzZmien6fCrr%2BNqamipZWptq6x0WeaqKVfqbyxtcJoaWlwaWd6tH6VZpmlmZmneqmt2KWcsmc%3D