I thought of that, but the shaft is driven when under power, and is driven by the rear wheels under coast. I've seen this happen with worn u joints, they are fine when going clock wise, but driven counter clockwise things get all out of whack.

I've seen the same instance with loose converter bolts.

I know, the driveshaft shouldn't come into play at rest. And bad joints should be noticeable when moving. And we assume that he has checked all the bolts under the car. Hell it could be a weak fuel pump at idle not putting out enough. I'd still check the driveshaft.

Just some things to check.