Hi,
We had that sink and learned about the sink faucet luckily before we had any problems.
At the heart of the issue is that the sink can be set into folding position in a couple of different ways. One of those ways can look right, but can have the very small nubby handle raised up enough that the cover then closes down on it and turns on the faucet.
We found the best way was to fold the tall part of the spigot to the left, and check the small nubby faucet handle to make sure BOTH that it was not sticking up, and was also closed all of the way.
See pictures in post #27 on this thread for some ideas on changeout on the sink.
https://www.google.com/url?q=http://...CrzM95ZD4ZzLvg