Did you spot the problem? Germany and Bavaria are not synonymous (this confuses the history of Bavaria's ancient Reinheitsgetbot, too); Cologne is nowhere near Bavaria.
But there is another issue, more subtle, more confusing. Is it an ale or lager? When I tweeted out that menu picture last night, a number of people said it was not just a mistake to call kolsches Bavarian, but to describe them as ales, too. They're sort of right--but that doesn't make them lagers, either. As with so many things German, the categories have been sliced more precisely:
This middle-space, Obergäriges Lagerbier, indicates a top-fermented beer that has been lagered--a lagered ale. This distinction is useful to the extent that it illustrates the dual nature of the word "lager," which designates not only a yeast type (a noun), but also the practice of cold conditioning beer (a verb). It harkens back to the era when yeasts were only dimly understood, but practices very well known.
But as much as I respect Ron Pattinson and his knowledge about German beer, this is a needlessly pedantic distinction--and one I had a hard time finding Germans observe. When I was in Cologne, I asked about Obergäriges Lagerbier, and got curious looks for my trouble. When I was touring the Kolsch brewery Reissdorf, I had an exchange with a brewer where I tried making Ron's point--and it was his point; I'd boned up on his vast treasury of blogging before my trip--but the brewer dismissed the distinction. "No," he told me, "it's an ale." I think the world has shrunk enough now that the notion of ale as Americans understand it is typical, even in Germany.
So you may call a Kolsch an ale without worry, or if you want to impress your friends, you can call it Obergäriges Lagerbier. You might even argue that since it's a lagered ale, the word lager can be used in describing kolsches (though not by itself).
Just don't call it a Bavarian ale.