Is it possible that there is something inside the tire (like water) or some other foreign items (like repair sealant that someone may have sprayed in)?

You should first narrow it down to whether it is infact the tire. That will save you a headache in guessing all other possibilities. If it was able to be balanced, you wouldn't think it would have something inside (ruling out my theory).

Other item to look at is if you have 3rd row seats, you may have the self leveling air suspension, which may have a leak - something else to think about whether it applies or not.

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SOLD - 08 X5 (Titanium Silver w/Black Nevada with all options).