Access Remote WordPress Install from localhost

I have a live WordPress environment running on a website. I use my local machine to develop the site and make changes to it before deploying it live. While trying to open wordpress/index.php, I am able to connect to the database, but somewhere between loading wp-config and displaying the site, the loading URI gets changed from localhost to the domain that the site is running on.

My goal is to be able to be able to have a copy of my WordPress install running on the local machine with access to the MySQL database that runs on the remote server.

Is this possible? How?

(the DB_HOST in wp-config has already been modified to not say ‘localhost’, the the DNS location of the MySQL server)