Or it could give people who are already suspect of government more reason to avoid the vaccine.
A stranger on the sidewalk is giving away free cookies. If in addition they offer $100 to each person who eats one, does that make me more, or less likely to accept a cookie?
I don't think the public's interest is in question here (well, at least not in this particular argument).
I think the point is about how much you trust the person handing out the cookies/vaccine and money. There are plenty of people who trust the government about as much (or less) than a random stranger.