It seems, that if vmWare vCenter 6.5 appliance is behind HTTP proxy, it uses this proxy only for HTTP connections. Thus update check fails, since it checks remote update site via HTTPS.
To fix this, enable SSH acces on vCenter server, connect to it, enter bash shell.
Enter valid http proxy address into HTTPS_PROXY (e.g. HTTPS_PROXY=”http://yourproxy” ) line
That should fix this problem.