Personally, I'd say that the issue is caused by 'some' over-heating. Just enough so to create such temporary, sudden out-of-the-blue stretched lines. Such visual anomalies are usually caused by the GPU's Memory being hammered by a lot of heat. On the Core side of things, when the Core over-heats, visually, the type of anomalies are 'dots', covering the whole screen, or parts of specific areas/polygons. But, yeah, when we talk about lines like that, then it's usually Memory that's over-heating.
It doesn't mean it is over-heating.
But as I said, I'd just bet on it.
And it actually makes sense if it doesn't do that in other games, since Oblivion is the only game currently available for the PC that demands so much juice from any GPU generations that it supports. Even Far Cry or Doom 3 don't "ask that much" from a GPU. I mean ... my X1800 XL is cooled with the infamous Zalman VF700-ALCu, and while it does indeed perform extremely well, my GPU's Core temperature at full load when playing Oblivion reaches 65ºC. And I play Oblivion at 1024 x 768, no A-A at all, and 8x A-F, all in-game settings highest, except for Shadows, which are completely turned Off. And HDR lightning is On.
I'd imagine that it'd be a bit more of a stress for a previous generation to run a game like Oblivion WITH some or a lot of A-A enabled, even without any HDR at all.
Like I said, the whole thing is just what I think. It might be something else. But you telling me that your 9800 Pro also suffers from the same problem then my conclusion is clear. Is that they simply both suffer from the same issue, in the same conditions; over-heating.