It proves nothing to you, I draw the lines of my perceptions to my own benefit.
I believe every bootstrapper has some kind of self-funding. So whenever I see a story of a successful bootstrapper, I assume self-funding, and I don't consider it dishonest in my perception of the story. If the bootstrapper happens to be a millionaire already, and the "self-funding" is in the order of hundreds of thousands of dollars, I don't consider the inspiration applicable to my own case, but I would probably not call it "dishonest".
All of your small-money examples look to me as in this category as both honest and applicable to my case.
One of the lines that I draw is that calling "bootstrapper" a company that received, let's say $100,000, from a billionaire in order to help with growth is dishonest in my perception.
From the tone of your comment, you seem to have the impression that I am a purist of some sort about the technical definition of "bootstrapper" and that I am policing how other people use it as some sort of crusade. You are wrong. I was sharing the filter that I use when interpreting this kind of story. I create these filters because I am a wanna-be founder myself, and I have decisions to make, decisions that are influenced by what I read about what happened to other people. I have to establish a gross probability of success with each decision. Deciding to pursue funding is one of those decisions. So when I read about bootstrappers I try to filter as honest or dishonest (also along other dimensions, as applicability).
So this search of mine of what I consider honest or not would prove nothing to you or to anyone. I don't care. It is not the reason I do it.