I'm new here. Can someone explain why places that are not in St. Louis give their address as St. Louis?

For example, this university says its address is in "St. Louis, MO 63141." But neither Maryville University nor the zip code 63141 are located in St. Louis. Tons of places do this, and as a newcomer, it confuses me. People from Tacoma might informally say they're from Seattle, but I'm pretty sure you won't see a university in Tacoma give its address as Seattle.

Is it just done so people associate the address with a recognizable city? Is it frowned upon? Is it referring to St. Louis County? Does it matter whether you send mail to "St. Louis, MO" or the actual city?