As I'm not near my parents, I decided to try the Fiddler Web Debugger with my Envy 5541 printer, which I know is working normally.
On printer startup it establishes two connections, one to xmpp008.hpeprint.com:5222, and one to chat.hpeprint.com:443. Both receive HTTP200 return codes.
I'm also seeing the following connections get established which I *think* are being initiated by the printer but I'm not 100% sure:
talk.google.com:5222
www.google.com:443
The above requests are repeated several times, and all get HTTP200 response codes.
This is followed by regular requests being sent to chat.eprint.com with the following text being sent as a POST request "POST /chat/shortReport?model=K7G89A HTTP/1.1". It also receives a HTTP200 return code.
If I force the printer to search for a software update, I get a similar situation to what you were finding:
h10141.www1.hp.com
GET /pub/inkjet/updates/nb/manifests/b_b_c_p00_ae588a0bceb43af0991579e2c775a435_ae588a0bceb43af0991579e2c75a435 HTTP/1.1
This generates a HTTP301 return code, and is followed by a request to :
whp-aus2.cold.extweb.hp.com OR whp-aus1.cold.extweb.hp.com
GET /pub/inkjet/updates/nb/manifests/b_b_c_p00_ae588a0bceb43af0991579e2c775a435_ae588a0bceb43af0991579e2c775a435 HTTP/1.1.
This generates the HTTP404 return code. The re-direct looks to me like it's being sent to a load balanced IP at the DNS name of the HP server is changing, but the response code is staying the same. To me this looks like the request hasn't succeeded. However, the printer responds that it is running the most up to date software.
So with my ENVY while the instant ink is working, I suspect that software updates are also broken. It does look to me like the ENVY printer is connecting to instant ink in a different way to Officejet printers.
I hope this comparison of the ENVY and Officejet behaviour proves useful to someone.