It looks fairly consistent in every browser I've tried. This is Safari 5.1.10.Around the time of me asking (Friday evening, UK), the line was very noticeable – more than in @AngerDanger's example – for at least one person whose avatar was shrunken so that the user-preferred square appeared properly shaped within the MacRumors-preferred circle.
In weight and colour, the line of the circle was comparable to the dashed line that's drawn above by redheeler. What I saw were solid lines, and I thought that I saw those circular lines around the shrunken square avatar of more than one person. But it's possible that just one person intentionally drew the circular line around their square within a square. Unfortunately I didn't shoot the screen; I assumed that everyone could see the oddity.
The circular line was not visible around a square avatar when I reviewed this topic at 18:07 yesterday, with @Porco as an example:
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An optimistic guess: maybe the circular lines were transient whilst site administrators experimented with a combination of auto-detection plus shrinking of square avatars.

Like @AngerDanger pointed out with the inconsistent outline on his avatar, there may be some rendering issues causing what you're seeing. Another reason that gray background should be removed (and different generic avatars chosen).
It won't appear where the avatar is shown as square, on user cards or profiles.