And I was almost ready with my business plan to start that company... You made me go back and start from scratch...
There is always plenty of room to make things very complicated.
The buyer could also have to send a short video saying "Today, 7-nov-2005, I agree to buy 1 year subscription of <Make me smile> magazine and receive it by snail mail using DHL."
That can replace the actual presence... somewhat.
But yeah, you are right, a plain signature wouldn't do it.
Well, you can still start the company, just change the specifics of the product.
Back to the main question, if a company decides not to take a customer, there is virtually nothing that the customer can do, aside from asking the company to make an exception in his/her case, and offer to provide any evidence necessary: ID copy, Card copy (most numbers blurred of course), order verification by phone, utilities bill copy etc., anything that would make them comfortable enough.