Depending on the fork, headset ect going no handed isn't always fun on a mtb. Think about it like this too. The knobbies cause a lot of wobble by themselves. This isn't proof of overall bike stability it is just the way it is. Stick slicks on the bike and get a better headset and I doubt you would have the problems.

You are also probably a little spoiled. A mtb will never feel as smooth on the road as a road bike.