I don't think they claim to be able to prove it. Or claim it to be a fact. They just believe it likely, which is as legitimate as believing it unlikely, IMO.
Not relationtional, the provable and the unprovable. Once you venture one inch into the unprovable, the sky is the limit, or might as well be. Now, small steps into the unknown may be provable over time, based on hypothesis, but modern science is nowhere near proving that either life can be created by random events, or that life exists on other planets. Until there's anything close to demonstrating either is possible, there's simply no reason to believe it probable. They're welcome to keep trying, but they have been for decades, and are no closer than when they began. At this point in history, life is still a miracle, and is only known to exist here on earth. From what we've seen so far, those are the only known facts, and they may never change.