So the best thing you can do to protect yourself and your trees is to ask for a license and insurance for the business and also if they have any references that you can call. Those Three things right there will separate the men from the scammers so to speak. There are a lot of them out there and they are just looking for a chance to take advantage of homeowners and they usually leave a trail of destruction in their wake. And never give money to any company upfront if you do your just asking for trouble.
In short the moral of this story is don't trust any one that comes knocking on your door telling you that they are working down the road and noticed your trees need trimming. This is one of the biggest scams around and I've heard about it from literally hundreds of people. So if your planning to hire a local tree service please do it wisely. For your own sake.