Is it necessary that these two readings be mutually exclusive.
No!
Good question. Very often ambiguous readings are similar, sometimes even systematically similar.
In fact, in some cases one reading is always a subset of the other. In this case, if John lifted the heaviest horse, then no other person lifted a horse that is heavier than the horse that John lifted-- whether or not the horse that John lifted is just the heaviest of the ones the group lifted, or the heaviest in the world.
This is an interesting example of an ambiguity because it isn't the same as a lot of textbook examples of ambiguity (for example, the "Mary saw the man with the binoculars" type, or the "Someone hates everyone" type). The ambiguity seems to be in the reference set for "the", but also based on where you put emphasis in the sentence.