The Rebecca Black saga in brief: Parents hire company to produce two cheesy pop songs and one cheesy video for 13-year-old daughter. Self-described “music factory” writes song including explanation of order of days of week. Daughter sings song. Producers auto-tune the bejesus out of it. “Music factory” unleashes song and promo on unsuspecting world. Video goes viral when critics trash it as “the most appalling thing on the Internet.” Girl complains of “cyber-bullying.” Then comes vindication. Gaga says she is a genius. Forbes declares her a millionaire.

In all this, it is that last fact that seems most unlikely. Can a 13-year-old singing sensation, laughingstock or not, really make a cool million with a crummy pop song and a boatload of YouTube clicks? The answer, alas, is no. Rebecca Black might yet be vindicated musically or culturally. But not financially: At least for now, she’s probably no more than a thousandaire.

Forbes’ back-of-the-envelope accounting went like this. First, it tallied up revenue from all of those millions of YouTube views. YouTube, owned by Google, grants artists 68 percent of the proceeds earned from advertising on the site through its Partner Program. Forbes figured YouTube makes about $1 per 1,000 page views. Thus, “Friday’s” 30 million page views (at the time: It’s now up to 43 million) implied $30,000 in revenue, with a cut of $20,000 or so for Black. Then, it added in the earnings from downloads of the new hit single. Forbes initially reported that the song racked up 2 million purchases on iTunes. If iTunes pays out 70 cents per download, and Black keeps all of the proceeds, it makes her a tween millionaire.

But there are a few problems with this accounting. First, the numbers. As for downloads, Billboard reports that “Friday” has sold just 37,000 copies, meaning the song has earned about $26,000. And as for YouTube plays, the number could be lower. Rates depend not just on page views, but also on how many people click on the advertisements. Thus, the song and video have earned perhaps $40,000 and counting—hardly chump change, but hardly $1 million either.

Then comes the all-important question of who is benefiting from such frothy pop nonsense. Specifically, how big of a cut is the Ark Music Factory, which wrote the song and made the video, taking?

Let’s pretend that Rebecca Black is not Rebecca Black, but someone like Katy Perry, working not with an out-of-nowhere vanity label like Ark, but a legacy label. She might have signed a contract requiring no payment up front: The company would write her songs, help her record them, and perhaps make a video or set up a website for free. If she did not look like a moneymaker, the label would have dropped her, leaving her with nothing but a few recordings, a video or two and perhaps some scant royalty rights to songs nobody would ever hear. (Fewer than one in 20 signed artists ever produce a hit.) But if she looked promising, her label would have spent thousands of dollars promoting her—getting her on the air, setting her up to tour with a bigger artist, and so on. If “Friday” hit, Black would have in essence worked to pay off her debt to the label.

This resource-intensive model is now under threat. Record sales are plummeting, and digital music sales are not yet making up the difference. Viral stars come out of nowhere. Labels are increasingly worried about pouring resources into unknown artists. With her—how to put it?— imperfect delivery, Black might never have gotten a shot.

Enter leaner, cheaper, more web-savvy new business models, exemplified by Ark, a business more like Barbizon than Atlantic Records. Ark runs casting calls for tweens and teenagers, handpicks a few, then has their parents pony up cash to offset or perhaps even fully pay for the cost of writing the song, recording the track, and making the video. It then acts as a promoter, manager, and record label, hyping the songs on the Internet and getting its young artists in front of industry representatives.

I contacted Ark to ask more about its business and its contracts, but got no response. (Tomorrow the company is scheduled to release a video called “The Truth About Ark.”) It could be breaking even or making money on song-writing and video production, charging parents hefty sums to make vanity videos for their kids. But my guess is that it is also taking a serious cut of whatever Rebecca Black is making on downloads and YouTube views. That means of that $40,000 Black might be taking home half or less.

Of course, viral videos never end up making their producers millions all by themselves, no matter how viral they go. For instance, the famed “Charlie Bit My Finger” YouTube video, the fifth most-viewed clip on the site, with 295 million views, apparently earned the family that made it in the tens of thousands of British pounds—plenty of money, but not millions. The advertising rates simply are not high enough to push into seven figures.

The value lies in the exposure: You don’t make money from a video, but because of it. If you have a hit video, chances are you can make plenty of money elsewhere—by winning a traditional-label contract, touring, making ringtones, selling merchandise, gaining endorsement deals, and so on. If Black is going to become a tween millionaire, the money will come from somewhere like T.G.I. Friday’s, rather than “Friday,” directly.

And Ark did make that happen for Black. So while there may be no valid defense of her song, there is certainly a defense of the lighter, leaner business model that produced it. Ark might make awful music. But it does give its artists a shot at the limelight for a reasonable fee. Reportedly, Black’s parents paid just $2,000 for the whole shebang.