Your summary is incorrect. Advertisers and users are mutually dependent. If the advertisers priorities clash with the users priorities, it is not at all obvious that the advertisers will win. The fact that Google mail doesn't have flashy colored intrusive ads is testament to that.
by this definition, the Rolling Stones are "the product" too then
Yeah, by what definition aren't they? Like any popular high-demand product they get to name their price.
But no gmail user is in much higher demand by google (or their advertizes) compared to any other. The generic gmail user is more like dime-a-dozen no-name bands that don't have even a whiff of the negotiating power against a label that the Stones do by virtue of being the Rolling fucking Stones.
s/gmail/whatever "you're the product" service in question/
The fans pay money and get the Rolling Stones in exchange - it's abstract (obviously you don't actually get the band members to take home with you) but nonetheless sums up the relationship quite neatly in my opinion.
But in this relationship the Rolling Stone have a lot of power and get treated excellently. I'd love to be that product!
The phrase you're the product! doesn't express anything meaningful about the relationship. Buy any magazine, you'll still get plastered with ads. In that sense you bought a product, and yet you still are a product. You still haven't discovered anything about the quality of the service.
Just to nit-pick: record companies have always "[sucked] up all the money". I don't believe there ever was a golden age where record companies were Nice Guys and everyone was happy.
"..people only made money out of records for a very, very small time. When The Rolling Stones started out, we didn’t make any money out of records because record companies wouldn’t pay you! They didn’t pay anyone! Then, there was a small period from 1970 to 1997, where people did get paid, and they got paid very handsomely and everyone made money. But now that period has gone. So if you look at the history of recorded music from 1900 to now, there was a 25 year period where artists did very well, but the rest of the time they didn’t."
In other words, advertisers come first. Since advertisers don't have the same priorities as end-users, I don't find the argument very compelling.