Definitely do not pay. I would not call, though, I would send a letter, along with a copy of their website showing free estimates, and that you wanted an estimate, NOT an emergency repair. Also tell what the guy said to you, why he was there a day early, and how irritated you were with having a contractor show up at your house on Thanksgiving day. Sounds like one of their employees may very well have written up a bill for emergency repair, when he did no such thing, so don't assume it's the company. Let them figure that part out.
In my area, I just learned today, the latest scam is a couple of Mexican men (don't mean to be prejudice, this is just what I was told) show up asking about doing carpet replacement job. They shoot cheap price. Then one sits at the table with the homeowners while the other one goes to "measure" the rooms. While he's measuring, he's also lifting items from the homeowners. Great, like we needed more thieves in the area! Last year this time, there was a car pulling up at houses, ringing the doorbell (dressed in suits, BTW) and when no one came to the door, they would look inside and if they saw anything handy to lift (i.e. laptop, DVD player, etc.) they would check the door and if unlocked, walk right in and steal!
Now, if I can convince my daughter to quit posting on Facebook the specific day I'm heading to see her this month! UGH!!! She's just so excited and not thinking about the ramifications if people know I'm gone. However, that being said, I also have some very nice (and nosey!!!) neighbors that will watch my place while I'm gone.