I did everything you mentioned and still get the same thing. I should be getting the HT2050 so I'll test that out as well.
The question to ask is which units are HDCP certified. Unless they are HDCP certified you can't trust them.
My bet is probably the switcher, as they are low cost and the very high cost of certification is skipped usually.
I used to have trouble with a Rotel pre/ pro that did not have HDMI. I found switchers to be bad news, at least back then.
What is the reason you are not using a receiver or pre/ pro? That would likely solve your problem unless the BenQ is the not certified. I know that using units not HDCP certified causes no end of trouble.
It cant ne the switcher if I plugged the DirecTV cable directly into the projector and the same thing happened.
In that case the BenQ projector is either defective or not certified. Ask BenQ if their units are HDCP certified and if so by whom. If they are not HDCP certified then dump them.
Just before I pressed the post button, I did a quick search. There are pages of stuff about BenQ HDMI issues. Just go to the AVS forum and see the complaints. My bet is those units are not certified and likely in the junk category.
When they said they "never heard of it", they lied though their teeth.