It really doesn't. Even the BEIR radiation safety council has had to admit recently that LNT has no scientific basis. (They refuse to stop using it out of 'an overabundance of caution'). And this is the institution that basically started and promoted the LNT way of thinking.

We know the basic mechanisms of cancer, DNA damage. We also know that on average each cell in the human body experiences around 10,000-50,000 single strand breaks per day due to...

Cellular respiration, ie Oxygen.

This fact alone kills LNT because in order to take LNT at face value you have to assume that radiation damage is cumulative and never repaired. If that were true, we'd all be dead.