Um, well, it's true - I am very happy to report! One of the tables on my 909 was adjusted all the way in, raising possibly the issue mentioned by Blue Shadow. The other was stuck and took a lot of (careful) effort to get it to move, like it hadn't been turned in a long time. It was set at about the halfway point, it turned out. This a great revelation to me (apart from making me feel pretty stupid, which I can live with). My Teac A-2000 has adjustable reel tables, with a screw on the face of the tables. I love that feature, and wished the Pioneer decks had it. Now, this is even better, because with the Teac you have to take the reel off to adjust it.
Thanks cnolanh and others for being kind enough to educate me (and maybe others) on this!