This isn't quite true. This is at least true of Comair, and I'm sure they have a union contract similar to others. The crew will get paid for the flight under the following circumstances:

1. Cancellation due to weather
2. Cancellation due to mechanical
3. Removal from the flight due to FAA flight rules (i.e. too much time worked for the crew)

I know quite a few FA's (mostly for Comair), and they have gotten paid for cancellations. I know one who sat in a hotel paid for by Comair for 2 days while her JFK flights were cancelled during this last snowstorm.

That is one of the very few upsides of the job. The union makes sure they get paid the time they're scheduled.

The downside is of course that if they sit at the gate without the door closed, then they do not get paid flight time but instead only ground/per diem time. In contrast, once the door is closed and they leave the gate, they're getting flight hours. And that time counts against the FAA duty day (which is why so many crews go illegal in the winter).

Of course, if the crew calls in sick or gets sick or hurt in the midst of a trip, there is no pay for the flights not worked. But if HQ cancels, the crew will be paid.