1080p HD channels from DirecTV Stream

Zero. Broadcast HD channels are either 720p or 1080i. 

Directv stream channels are delivered in 1080p for 1080i channels and 720p for 720p channels. 
if you have a Osprey DTV stream box hold down the dash button until the general info screen comes up. It shows the streams video info. 

That may be the resolution output by the C71K box, but the actual broadcast/cable channels are 720p or 1080i. 

If that is the case, who is broadcasting 1080p HD ?

Then again, which channels are 1080i ?

720p is pretty much antiquated, whereas 4K Ultra is the extreme high end, I would have thought with today's availability of broadcasting bandwidth 1080p should be the standard.

There are no 1080p broadcasts. ABC & Fox are 720p, NBC and CBS are 1080i. Some streaming devices and TVs will automatically upscale to either 1080p or 4K, but the actual broadcasts are 720p or 1080i.

Per professional reviews of the service, I don't think DirecTV Stream sends 720 or 1080i necessarily:  "A representative from DirecTV Stream stated that the service uses an adaptive bitrate that maxes out at HD."

This seems wish/washy language to send less quality than sent by the broadcasters being streamed.

DirecTV uses adaptive broadcasting.

You'll mainly notice the changes when you first change a channel. I'm not sure if the channel first connects a SD, but it does adjust to your particular bandwidth with a demand buffer built into their system on specific channels 

And translated into English, I suppose that means if the direcTV servers are being heavily used, they may send a lower bitrate and maybe I won't get 720p (or 1080i) on my 65 inch HDTV?  

In other words, it is not just my personal residence bandwidth - -is it?   Or with my fiber 500/500 mbps Internet service should I ALWAYS expect the adaptive bitrate algorithm used by DirecTV to send me 720p (or 1080i) -- if that is what is being broadcast?   

It's "adaptive" based primarily on your own internet download speed. Slow internet connection will yield lower video resolution. With a 500/500Mbps internet service, you should always get the actual native resolution (720p or 1080i for HiDef and 480p for Standard Def). Of course, the download speed at your actual streaming device might be slower, especially via WiFi.