In spite of what we may think of desktop database applications, and in particular Access, many organizations have a significant investment in Access, and Access applications. As those organizations grow, their need for concurrent data access emerges and grows. Access can no longer do the job. What to do? Rather than develop a new application front end, the data can be migrated to larger more scalable solutions, and the front end can remain in Access. Since at least v.2003 Access has supported using an MS SQL server backend, (and while I'm sure not technically supported, I suspect through ODBC, a MySQL backend as well). Said organization may also have an investment in other open source products such as Apache and PHP and talent to support them, so rather than incur the expense of MS SQL server licensing and support, why not utilize MySQL. Conceivably a web front end could be developed to replace the Access front end, but that's more time and money for said small organization, in addition to the time required for user familiarization training.
Another case that come to mind is what I have heard referred to as the Layer 8 requirement (i.e. "because the boss wants it"), or the chair-to-keyboard interface requirement.
And while also not a legitimate business case, sometimes we techies just like to climb mountains because they're there.