Your story doesn't sound that different from https://news.ycombinator.com/item?id=27400221, tbh, other than the driving 100 miles and the Trumpian bits, which aren't relevant to the ethical question.
It seems to me that the important information would be: did anybody who was eligible fail to get vaccinated as a result of the extras dropping in? In your story the answer is no. In the other dude's story, it seems like we don't know. If his story is accurate then the answer is probably not because otherwise the people running the site would have told him "please don't do that because it might take doses away from the eligible". But who knows.
It seems to me that the important information would be: did anybody who was eligible fail to get vaccinated as a result of the extras dropping in? In your story the answer is no. In the other dude's story, it seems like we don't know. If his story is accurate then the answer is probably not because otherwise the people running the site would have told him "please don't do that because it might take doses away from the eligible". But who knows.