If licensing costs are an issue, I was going to suggest you try one of the free alternatives out there (MySQL springs to mind, and should provide a backend for Access easily enough), but if you have no choice in the software you use, this may not be possible... Also, OpenOffice now includes "Base", a database program which looks similar to Access, but won't have all the frills (I've not had a good chance to look at it yet).
The reason people advise not to use Access in a networked environment is that it has a relatively small number of maximum users compared with many "heavyweight" database applications. Now I don't have any current info, this is for Access 2000, but MDSE (the embedded version of SQL Server in Access) has limitations; 2Gb database files and its fine tuned for about six simultaneous users. According to Microsoft, MDSE is suitable for small workgroups (five or less), but the actual performance is down to the machine specs. Even a low spec server (should) be fine with about 25 users. So they may have a point; it depends on how big your DB will grow and how many simultaneous users you will have.
Heresy in a Access forum, I know.