Concurrency Clarifications

I'm redoing a patient info database for a healthcare facility (right now it's a flat Filemaker db with 869 fields and 4000 records) and I had pretty much decided to move it over to access but I was talking to one of the database guys at the local University and he mentioned that if there is going to be more than one user editing data that I shouldn't use access and should use mysql instead. Then after talking to a different guy and reading through this forum it seems that sharing the database shouldn't be a problem but I just wanted to get a few clarifications first.

There are only 5 or 6 people that would be accessing the database and I doubt that they will be accessing the same records at the same time very often. Basically, what I want to know is can I setup the db with access so that those 5 or 6 people can access it whenever they want and add and change records. I'm not familiar yet with how splitting the db works but could I just put the db file on the network and they could just open it in access and make whatever changes or do I have to split it. Thanks for any advise.