Here it's not the service that you need to trust. The service is just that - a service.
The trust issue is about the blockchain. There's enough literature and enough security material written about the blockchain and the technology behind it to conclude with absolute certainty that the document for the hash existed at the time the hash was entered into the blockchain.
I recently posted in the Bitcoin thread a link to a blog post that walks through the mathematics underlying blockchain security. It's extremely well written and highly accessible to anyone with a little bit of understanding of mathematics. https://www.donation....msg366595#msg366595
I think it would be extremely difficult for a judge to rule against a hash entered into the blockchain being admitted as evidence. He would in effect be saying that logic, mathematics, and science have no place in court.
Here's a graphic to help illustrate the kinds of numbers that we're talking about because they are so big that they simply cannot be imagined. i.e. 2^256Service: Proof of Existence
To throw out blockchain evidence, a judge would in effect be saying, "Yes, it is possible that someone forged a 1 in 2^256 probability with the forgery exactly matching what we are talking about here today."
Now the thing is that if you were able to forge a hash, the original source would be gobbledy-gook, and not a coherent document. So the probability again skyrockets beyond comprehension.