Yes, the problem with the cube at the US Open was the fact that it had a side with no stickers at all. Applicable rules:
3f) Cube puzzles must either have coloured stickers or coloured tiles.
3k) Puzzles must be clean and must not have any textures, markings, elevated pieces, damages, or other differences that distinguish one piece from a similar piece.
And yes, they are very lenient about the rules on cubes at the competitions, apparently. But honestly, with the attention they're trying to get for cubing, it's probably for the best that they're that way. They can start to tighten up the rules if cubing ever becomes more popular, but for now, there's no point in discouraging potential competitors over minor rules infractions.
I remember when I first entered the US Open, I was worried about these rules and afraid that since some of my stickers were a little damaged, I might be disqualified (because the stickers might "feel" different - could be perceived as an advantage for BLD, although anyone who's ever done BLD knows that's just silly). But I got there and found that they didn't even check the cubes at all.
I think the best solution for this if they need to start to get more strict is to provide stickers at the competition for anyone who needs them. And I know that at many of the competitions, they do just that.