Here is an issue with Infopath browser forms accessing data in SharePoint via REST web service over SSL.
When I entered the REST url as https, InfoPath throws the following error: "The Internet address 'https://site/_vti_bin/listdata.svc/listname' is not valid."
When I used the http REST url, InfoPath takes it without any issue. Infopath form loads fine in client.
However, when I load the form in the browser, the following error was thrown by InfoPath: "XML data that is rquired for this form to function correctly cannot be found. " And I see "401 unauthorized" error in the ULS log.
I have configured AAM to map both http and https internal urls to default zone, public https url.
Set the DisableLoopbackCheck registry entry to 1 to ensure SharePoint can make a loopback call to itself.
You've omitted the key point that you had this issue while testing on the server. If you had this tested from another client, you wouldn't have had it.
Alexey, thanks for the comment. Since I was developing InfoPath on the client, this issue was in fact discovered on a client machine while developing an InfoPath form template that gets SharePoint data via REST service over SSL. The fix was applied on the servers.