Responding to someone actively expressing interest in your product by offering them a demo definitely doesn't qualify as "turning it into a greasy sales pitch". They've clearly built the product to be a low touch experience so offering to run through it with someone is actually very pro-active of them.
Same with my dentist that I started going to 2 years ago. I live in a differtnt country now and literally book appointments 3 months in advance with them just so I don't have a bad experience with someone else.