That connection information does appear correct.
In researching the error on the MySQL site: http://dev.mysql.com/doc/refman/5.7/en/gone-away.html
I see the 3rd listed cause is: "A client application running on a different host does not have the necessary privileges to connect to the MySQL server from that host. "
I really feel like that has to be the issue here. It isn't a problem with the PowerCMS code itself, it is an issue with not being able to connect to the remote database because of a permissions issue of some sort. I don't think there is any code that could be updated in the php to correct this problem, it would have to be fixed by your server administrator adjusting the permissions.
I'd suggest just using a local database for testing locally and export/import the data when you are ready to go live. I know it would be nice to be able to use the live database on your localhost, but it appears that isn't supported based on the error and response by your server support.