Correct, the burden of proof is on the company that is supplying the electronic service. But it is not that they 'decide'. They need to collect required types of evidence (that do not conflict with each other) in order to prove where their end customer is. Accepted evidence includes the customer's IP address; their fixed landline; their mobile phone SIM card country code; and credit card billing address. VAT is based on where the service is 'consumed'. That German person who resides in the UK will have to pay UK VAT on any electronic service that they consume in the UK. There are a whole host of other rules if that person goes on holiday in the EU.

EDIT: If some of the evidence above 'conflicts' with the other, e.g. UK fixed landline but a German credit card billing address, then more evidence will be required until the merchant is satisfied as to the customer's precise ___location.