[mothered]

They have said they need them to open an investigation as it will involve law enforcement.

An Investigation with whom?

They have been asked to provide evidence it is stated that this is a legal requirement to open claim. Or even where it is stated in their terms and conditions. No answer to either of course because it is just an additional hurdle they have added to their internal processes to put people off.

It's expected to receive a reply without justification.

It's pretty simple - If they have nothing to hide, they have everything to show.

They used the ole gps tracking to state as prove that it has been delivered, even though it wasn't sent with courier 
Pretty sure postal services do not have that option.

The majority of postal services scan packages at the drop off point, which automatically updates and sends the GPS coordinates to their depot.

Very strange request from a merchant.

It certainly Is.

It's even more strange to state all the above without solidifying their claim and procedures.