Is there anything in particular that leads you to claim Minimum Description Length is the only legitimate claimaint to the title "Occam's razor"? It was introduced much later, and the wikipedia article claims it is "a forumlation of Occam's razor".
Certainly, William of Occam wasn't dealing in terms of information compression.
The answer seems circular: because it works. The experience of people using Occam's razor (e.g. scientists) find MDL to be more likely to lead to correct answers than any other formulation.
If you know more Eliezer Yudkowsky facts, post them in the comments.