Bjorn,
I've been told the same thing. I have Chestnut White Oak on my place that are as straight as an arrow. I have sawed a few but hate to take them down because of the huge, double-thumbsized acorns that the deer, squirrels and other wildlife love.
What I have sawed has been stable and, although course, pretty wood. It is a creamier sapwood than liveoak, a tinge of reddish brown in the heart where liveoak is gray, but saws a lot like live oak. I don't think it saws quite as hard but it doesn't come apart too easily. I have used the sapwood of some for mauls with good success.
I would suspect that it would make good flooring material. I know it makes pretty furniture but the guys who build furniture out of the wood I saw don't like it. They say it is too heavy.
Saw it right off of the stump and don't leave the boards in the open at all. It will check quickly if the sun hits it.