Sounds to me like the tuning problem you are having may be due to pickup height. If your pickups are to high it will pull on the string causing an oblonged oscilation of the string when you pluck it. If that doesn't make sense, then imagine this - when you pluck a string, it vibrates in a circular motion. If the pickup is too high, the magnet field will actually kinda tug on the string at the lowest point of this circular motion causing it to be more egg shaped.

Now, you might say, but then wouldn't it do it to every string?

Well, not necesarily, you see the low E has more mass than the other strings and is therefore affected by the magnetic field more than the other strings. Try to lower the bass side of the pickup, just a half turn at a time till the problem goes away. If you end up with a wildly slanted pickup, then you've gone too far and it's time to check the other pickups. Usually the offendind pickup will be the neck pickup as that is where the the circular motion of the vibrating string will be at it's largest size occcuring over the pickups, therefore making it more vunerable to the tug of the magnetic field. Also, this is usuall more of a problem with single coils than humbucker as the magnetic feild of the single coil in more narrow and there a lot more focused.

Oh yeah, and this is an easy one...try tuning with the other strings muted. Sometimes you can pick up overtones from the other strings when tuning, therefore confusing the tuner.

Hope this helps.