I believe it comes down to a lack of experience. Experience on the part of the service techs. And I dare say any dealer tech that would take the cold beast for a test run is required to wear a full helmet. In my case, I too will need to resort to a sound track recording.
I had mine in, early on, for the problem and it was then sufficiently prolonged and loud enough for a half-assed fix. Of course this was Triumphs decision. A partial fix included only the lower sprocket and the tensioner. This pseudo fix lasted a very short while, until the next time I wore a half helmet, and the symptom was heard once again. Since then, I've had it back twice; for one short overnight assessment and again on a near three week stay, principally for another issue, and both times the techs "heard nothing" out of the ordinary.
At the time of mine having the sprocket and tensioner replaced, along with the sprocket/crank key, I jumped to the conclusion it was the key, as it was sufficiently beat up, with the edges rounded. This has since been argued against.
To my knowledge, those who've had the benefit of having the entire shebang replaced, including chain and upper sprockets, have not had a recurrence. ???
I believe your's is the first 08 Touring

Maybe a first clue is their reference to motor instead of engine.

Make an appointment for an overnight assessment. Have the problem specified on the work order.
Perhaps it's time for a class-action suit? Surely there are a few legal minds out there?