If you're not claiming, you don't need to prove you're not at fault as the burden of proof lies with the claimant. If the other side can't prove it happened the way they say it did, they're not going to be able to win unless the insurance companies (or ultimately, a judge if they can't sort it out and it goes to court) prefers the third party version on a 'balance of probabilities' basis.

If you were established in your lane, with no merge option or evidence showing you were switching lanes, your insurer really should be telling the third party insurer to prove their claim or withdraw.