We had an ADT lady at the door, she was polite enough although definitely pushy. Before I had said anything she was practically in the door taking her shoes off! She kept asking if she could call again later until I said quite firmly that I was in the middle of cooking my children's dinner, my washing machine had just broken, and it was generally a very inconvenient time. She quickly left.

I would just never buy anything off a cold caller. I generally find cold callers very annoying because it always seems to be at tea time or my children's bedtime. I am not a rude person so I try and be polite but they just don't seem to take the answer 'I am feeding my children/getting them ready for bed' seriously. "Just 5 minutes of your time" they say, like I can just leave the kids waiting for me in their pyjamas for their bedtime story...
And lastly, why would I invite a stranger into my house? Even if they do have a badge, it could easily have been mocked up.

So I can understand why people do resort to being rude - I know they are just doing a job but they often just don't take no for an answer.