I thought the same, then when I went for a vacation after receiving my brand new work permit, they did ask for it at the boarding! The agent looked at my passport, asked what is my status in Canada, and my husband replied by habit that I was a visitor. The agent went to talk to someone else before I had the chance to correct my husband, then he called someone on the phone, then talked to someone else again, then finally came back to us, saying, that there was nothing wrong, but he had to further check some things. At this point I was able to tell (and show) him that I had a work permit, he seemed relieved and assessed my passport and boarding ticket right away.
So, yes, indeed, sometimes the airline is concerned of the status and if the person will be able to return Canada. But of course that doesn't mean that once you are allowed to board you won't have any problems with the CBSA, that's a different story.