Skepticism is healthy, but I think he really has it.
It seems most likely that he picked it up at an event last Saturday. After his diagnosis was announced, a bunch of people who were also at that event announced positive results. They would all have to be in on it. But besides that, Trump loves to project strength. Going to the hospital isn't a good look, especially so close to the election. If it's all fake and some attempt to get a sympathy vote, I'd say it wasn't thought out well, because what it has done is put the virus even more in the news. Trump is very polarizing. I think most people want him to recover, but well wishes don't always equal votes.
When you hear that he received antibodies, remdesivir and dexamethasone, it makes it seem like they are throwing everything they can at the patient because they are in extraordinarily bad shape. But this isn't an ordinary patient, and I think it's quite possible that they are bending the criteria a bit in his case. So far, we have seen a few photographs, some videos that are a minute or three in length, and a brief car ride before returning to the hospital. That is not that much to ask of a significantly ill individual. He is not running a marathon or golfing 18 holes.