It's not that people think they are legitimizing something by purchasing it... not at all. It's that people think something is legitimate because it costs more than free. All this applies to before the sale, not after (in this case a "sale" is also someone downloading something for free).
I think ultimately you have to put yourself in the shoes of someone who doesn't know anything about making music or the music "industry" (or scene or community or whatever you would call it). I'm not trying to be condescending by calling people "listeners" or "common consumers," I'm just trying to underline the fact that we think very differently from people who don't make music. If I told a friend of mine that I make music, but that I give it away for free and I play shows, but they are free shows, they would probably think I'm an amateur (in the negative sense) and that I must not be very good if people wouldn't pay to see me. Moreover, if I told my mom that I make music, but I don't make any money from it, then she would say that I'm an amateur and that it's not a real profession because people aren't paying me for anything. They would be jumping to a conclusion, and have no idea of my real reasons for doing so, but when you put your music online and someone happens across it, there's no explanation attached... the conclusion they would jump to is all they have.
In the end most people define "professional" vs. "amateur/hobbyist" as whether or not you make money from it. That applies to everything. And people think professionals are better than amateurs.
In thinking about this more I know what legitimizes something for me... what people say about it. I knew little-scale was worth checking out because a lot of people were saying he makes great music and that I should go get "Error Repeat." The opinion of others, especially tastemakers (blogs, DJs, etc.) and more importantly, my friends, is what influences which bands I'll check out and what I think of them. I don't like The XX, but I know a lot of people who do, and therefore I consider them to be good at what they do, because they have a lot of fans.
It's interesting because in the end, I think that's the real answer to the issue of "what makes a song legitimate," what people think of it. But this is an interesting discussion because it makes you think about the attitude people have towards free stuff vs. not-free stuff... "someone's giving away perfume? Must be some new product or maybe it's not very good. Maybe I won't even bother taking one." vs. "This perfume costs $500? Must be high-class stuff! I wish I could afford it." In the end, this still applies to cases where a potential listener comes across something they haven't heard of, and none of their friends have... in that case the "what people think of it" doesn't apply at all, unless it means people don't think of it therefore it might not be good. Then it becomes a matter of how it's packaged... is it on a record label? How much does it cost? What's the cover art like? etc.
That's the last I have to say for this... as I said, it's not really the answer here, but I think the argument has some valid points.