Good point, I had missed this previously.

It seems that there exist a number of categories of services and each has its own rules for determining where the customer is located. If the service do not fall within on of predefined the categories the below rule apply, meaning that billing address is not enough and secondary verification is needed. It seems that most Saas service fall under the below rule. [0]

Where the digital services are supplied other than in the circumstances listed above, the business making the supply must obtain and keep 2 pieces of non-contradictory information to support and evidence the member state where the customer is normally located.

[0] https://www.gov.uk/government/publications/vat-supplying-dig...

Not from my experience. Many stores allow to set a different country as shipping address too (e.g. Amazon UK).