@James Ainsworth
Bullet number 2 i your list would be closest to what is our case although the customer themselves don't know on which server they reside. They all use the same service but it's installed per server (not cloud service) so connecting the asset to the server won't be an option.
We host a number of customer's websites and databases in our hosting centre. In order to be able to make quicker support we would like to automatically get server, os, DB, software versions etc. fetched when the customer places a support ticket. That way our analysts will save a lot of time and we can also see if that customer's server has any special settings applied which we need to consider.
We can of course have that information in the organisation but that would be a waste of a good asset management system :).