How are they using the spreadsheets? If only one person can use any given sheet, the amount of data is very small (under 64 Kb), and the spreadsheet addresses their processing needs then I don't see anything wrong with it.
Most likely they do not know the difference between a Spread sheet and a DB. ( I have seen this before) Or they once opened up Access put some info into a table and couldn't figure out where to type in a formula so stopped using it. ( Yes, a true story) So you could make a quick DB based on the Spread sheets, show the powers that be how wonderfull you are and increase your value. ( maybe pay ?)