For most of the sites, the software was reading the text-based "hand history" to collect data. When hands were mucked at showdown, the contents of the mucked hands generally appeared in the plain-text hand history (and most UIs provided a way to view them or to replay the hand action-by-action).

There were a couple of sites where this wasn't the case, or where the hand history wasn't provided in a simple text format (or at all) -- but generally, that's how it worked for the majority of the poker sites/clients.

The reason for being able to view mucked hands (at showdown) is because you can do the same in live games, at least that's the house rule in the vast majority of live rooms. It's almost always frowned upon, to varying degrees, to actually request to see a mucked hand - but generally IS allowed by rule (ie WSOP events explicitly allow asking to see hands mucked at showdown, though an 'anti-abuse' discretionary clause is included in that rule, too).