"Instead of creating Access databases on a file share, people use SP "lists" to store data"
This seems like a better situation than with Access though; at least the Sharepoint list apps are all located within one system; not as discrete files that may be scattered across laptops, desktops, email accounts and server shares, with who knows how many versions.
Agreed, and SharePoint tends to be backed up on the DBMS backup schedule, which is usually more frequent than the file-share/NAS schedule, which is another bonus.
It's the "non-sanctioned" aspect that tends to cause issues down the line, not moving to SharePoint from MS Access. I could've been more clear in that section of my comment.
This seems like a better situation than with Access though; at least the Sharepoint list apps are all located within one system; not as discrete files that may be scattered across laptops, desktops, email accounts and server shares, with who knows how many versions.