Searching for file within Time Capsule
Searching a TimeMachine backup is tricky - for one thing Spotlight has not indexed the backup (do not tell Spotlight to do this - you will be in for a world of hurt)

Second, you are sort of correct about about TimeMachine being virtual.  what it really is a hundreds of symlinks that link about in all kinds of crazy ways.

Your best bet, is to mount the volume using TimeMachine and recover the file using the interface Apple has provided.

If you are not going to do that, then hopefully you know where the file should be on the original system, and you should navigate to latest/path/to/file.html  where "latest" is the name of one of the directories in at the root of the TimeMachine archive.  Really it is...  If you know what date you want the file from, you could use that date in place of "latest"