Debian Configuration :: All Users Not Able To Write To USB Stick

I have a USB stick, formatted as FAT32 and I assumed that everybody would be able to read from and write to it. However, I find that if more than one person is logged on to the machine (logged on locally, with "Switch User"), then only one of the users is allowed to write to the stick, and the other users are only allowed to read from it. Is that normal?

Here's the scenario: person A logs into the machine, is in the middle of something but gets called away and the screensaver kicks in. The screen is now locked. Person B comes to the machine to quickly copy a file onto a USB stick, doesn't know person A's password so does a "Switch User" and logs in as themselves. They plug in the stick, can read from it, but can't write to the stick at all. Permission denied.

By doing a "ls -l /media", person B can see that the stick is mounted but is owned by personA with permissions drwxr-xr-x . So only person A can write to the stick. I haven't done extensive testing but it seems to be the person who logged on first who gets to own the stick. It's certainly repeatable as described above. And it's really annoying, because unless person B knows the root password, he can't write to the stick. As a real last resort person B could reboot the computer but he doesn't know whether person A has any important stuff open or not.