What brand of disks are you using? Does this happen on more than one machine? Floppies are not that reliable and neither are the drives. It's very unlikely to be anything to do with the operating system. My tips would be: always buy branded disks (same goes for blank CDs). It's not worth saving a few pennies if it will cost you in the long run. Always reformat a floppy before using it. Again, it's not worth "saving" a minute or two. Never use a floppy as the sole repository of important data. And keep them away from magnets, sunlight, extremes of temperature, humidity, etc.
Oh, and the network guys are telling porkies.