Connect to Server DB from Localhost Site

Believe it or not, I’ve searched in this forum and can’t find an identical situation to mine…

I have a WP 4.4 site running on my web server, which runs perfectly. I downloaded the site and would like to run in on LocalHost from Visual Studio, but connect to the database on the server. So, I haven’t made any changes to the connection settings in wp-config. However, when I run it from VS, it says “Error establishing a database connection.” Like I said, it’s a carbon copy/paste from my site to my local project folder, so it can’t be a credentialing issue or anything like that. The DB_HOST variable is set to an actual reachable host (mysql123.mywebhost.com), so it’s not “localhost” or a physical local drive on the server or anything. Anyone have any suggestions I can try?