Your reply was interesting, since reading it I went back to my Yamaha receiver & Roku. What I am experiencing is just the opposite,.......
You’re not experiencing the opposite.
In short, if u shut-off the receiver, Roku has to be set to Stereo from Home/Setting Menu. In that case, you’ll hear sound from all channels & contents thru ur TV speakers.
Roku will only pass-through 5.1 DD if the content is in 5.1 audio and Roku is set to 5.1 audio from Home/Setting menu. In that case, if u shut-off the receiver you will NOT hear any sound from ur TV speakers because ur TV doesn’t decode pass-through (bitstream) 5.1 DD & Roku will not detect ur TV & Auto-output 2ch PCM(Stereo) as w/DirecTV & Blu-ray!
Your experimentation is correct & sound is heard from TV only when Roku streamed content in a Stereo, however my previous replay was kind of short (I assumed u were familiar w/DD/DD+ Decoding).
So, if you planning to shut-off the receiver, Set Roku to Stereo from Home/Setting menu, this way the receiver will pass-through audio signal in Stereo instead of pass-through audio in 5.1 DD.
Note: Amazon is the only channel from Roku1 (that I know of) which offers 5.1DD contents.