Did Giants low-ball Lincecum to save San Jose?

So why are the Giants and Tim Lincecum so far apart? Andrew Baggarly thinks it's about more than trying to save a few (million) bucks:

    We all know that Magowan’s replacement, Bill Neukom, has positioned himself for a major battle over preventing MLB from overturning the Giants’ claim to the South Bay. Last year, the Giants even bought a portion of the Single-A club in town. (And have you noticed the San Jose Giants are even switching uniforms to look more like the parent club next season?) The Giants have been murkily tied to efforts from the San Francisco City Attorney’s office and a local coalition in San Jose to prevent the A’s from relocating, too.

    The reasons for the bunker mentality are well known. The Giants attract a significant percentage of their corporate sponsorships, season-ticket and suite sales, ballpark advertising revenue, etc., from companies in Silicon Valley. Their ownership group is a who’s’ who of the tech sector. It’s part of their identity as well as their bottom line. They simply cannot afford to let the A’s cut into their interests in Santa Clara County.

    And what’s the only way their territorial rights can be overturned? A three-quarters vote of the 30 major league owners, who’ll basically do whatever Commissioner Bud Selig tells them to do.

    How does Lincecum and his arbitration status enter the equation? It’s simple. The No.1 way to tick off baseball’s owners is to establish a new salary threshhold. And Lincecum has a very good chance to clear Ryan Howard’s $10 million bar for a first-year arbitration player.

I don't want to argue with Baggarly's logic, so instead I'll argue with the (presumed) Giants' logic ...

They filed at $8 million; Lincecum filed at $13 million. Let's assume for a moment that the Giants' figure is artificially low. Doesn't that increase the chance that Lincecum will clear the $10 million bar? If the Giants had filed at $9 million or $10 million, wouldn't they have a better chance of winning the case?

Or maybe the Giants didn't figure this thing would go to arbitration (most of them don't). Maybe they figured they could file at $8 million and Lincecum would file at $10-$11 million and they'd settle around the mid-point, which would have been shy of the Ryan Howard Bar.

This all seems a little complicated, though, doesn't it?

My guess is the Giants just filed the wrong number. It happens.