I must say that the exact same thing is happening on my HP Veer when charging wirelessly. It is not a faulty charger, but a known issue.

While it may be connected to the charging itself, argumentation with how Qi charging works is not relevant. Unlike Qi compatible phones/covers I know of, HP (Palm) phones have a magnet (and so does the Touchstone) so they snap right on the charger and stay there in a non-horizontal position. It is a fair assumption that the reason why Qi compatible phones do not have touchscreen problems while charging might be the lack of such magnet.

AFAIK all Touchstone compatible phones have such passive magnet and all of them suffer from this issue.

I don't have the Veer with me right now, but it might be interesting to check if the problem occurs when the Touchstone is not plugged in a power outlet.