Some of this is correct but it's too much of a simplification. Firstly; and most importantly many times Jimmy Page has 4 or 5 layers of guitars playing the same part to give it that thick and heavy sound. For an example if you listen very closely to Black Dog it has one guitar part but that one part is made up of multiple layers of different performances of that one guitar part (probably 5 layers.) You can hear this same approach but with less guitars on "In My Time of Dying" where two different guitars play the same part. One has a fuzzier tone and one has a cleaner tone. Listen to it on headphones, which makes it easier to hear them.
Secondly, many times Jimmy Page would have a guitar-army arrangement with many guitar parts going on at the same and because he was only one person he had to overdub them. Songs like "Celebration Day", "Trampled Under Foot", "Dancing Days", "Ten Years Gone", and "Achilles Last Stand" are all great examples. The first four start to sound a bit muddy because of the multiple guitar parts and layers of tape hiss. By the time "Achilles" comes around apparently tape noise reduction got good enough were it wasn't as much of a problem That's why Presence is probably their cleanest sounding album.
With analog there are two things to worry about. The first is generation loss which is when you copy one tape to another tape when bouncing down multiple tracks to one track to free up recording space, as described by the post above. The second is the loss that occurs every time a piece of analog tape runs through a machine a little bit of the magnetic material is worn off in the process. Queen faced this problem when recording "Bohemian Rhapsody." They even joked about being able to see through the tape by the end of the recording session. Fleetwood Mac (with Rumors) and Pink Floyd (with The Wall) tried to address the issue of tape wear by recording the rhythm tracks on a tape then copied that tape to work on. After all of the other work was done they then went back to the pristine rhythm track tapes to finish the work by bring in the overdubs at that point so the basic rhythm track tape didn't have to go through the machine over, and over, and over, and over again. For the Fleetwood Mac Rumors sessions they discuss that work flow extensively on the Classic Albums documentary that covers it. It's a good DVD if you haven't seen it. To my knowledge Jimmy Page never used this pristine rhythm track method with Led Zeppelin, probably because it would have slowed down the recording process and disrupted his creativity too much.