Ok, figured it out, snowflake's install odbc documentation is lacking a little. For whatever reason Installing the RPM Package steps worked. Turns out there is a note in there:
"The installation directory is /usr/lib64/snowflake/odbc/ . You’ll need the location later in the instructions."
Probably obvious to lots of people, but /usr is accessible to any user. Versus the TGZ File steps do not hint at the odbc's location being significant when it comes to multiple users.
I originally was following the steps for the TGZ File:
"Copy the resulting snowflake_odbc folder to the directory where you want to install the driver. Make note of this directory. You’ll need the location later in the instructions."
In the case of multiple users on rstudio-server, turns out its significant where this folder sits. So one might still use the TGZ File, as long as they had a clue about where to copy it to.
I got the RPM package to work, so I'll stop there.