If the laptop in question is one of the newer thinkpads (eg., t430), then there is a separate "night light" next to the webcam (called a "thinklight (tm)") which is unrelated to the webcam. The webcam actually has a smaller green light that indicates if the camera is on. The bright white "think light" is there just to illuminate the keyboard in "less than perfect lighting conditions" (from t430 user guide, t430_ug_en.pdf).
To turn on/off the "thinklight", press "fn + spacebar" (this also works under linux mint). This might be easy to accidentally trigger, especially if you also use gnome-do (which I do), which I have mapped to "super+space" (i.e., "windowskey+space"). (Note: and for the t430, I've also remapped/swapped (via bios) the fn & ctrl keys, making it even more likely to accidentally trigger the "thinklight".)
To see if the webcam is actually on, you can install the package "cameramonitor" (as per package description: "designed for GNOME, but should work as well on KDE and Xfce"); it checks to see if the device is active & reports (via system tray icon / graphical notification) when the camera turns on/off.