This is a very hard problem to solve, and people have tried.
Let’s say you do as you said: hash the data (screenshot, date, etc) and upload it to a trusted server. Nothing can stop me from generating fake data, hashing that and uploading it instead.
Ok, so maybe you decide to add a cryptographic signature to prove that it was the web browser that made this hash, not an unauthorized one. That might work for a while, but the private key needs to be shipped with the browser software, so a sophisticated person could extract that key and then generate fake data. Especially is the browser is open source (like most are).
Alright, what about if we add a special chip on the device that is hard to tamper with and keep the private key on there and do all the signing on that chip. Those do exist somewhat already, but hackers have found ways to break them.
Ok then you move everything to the cloud. Have the entire web browser running on a cloud machine by a trusted authority. Maybe then you can do what you’re discussing, but you’ve also entered a privacy nightmare where everything you’re doing can be monitored in real time.
What would be a better situation (and where I think we’re going eventually with Gen-AI) would be to put the responsibility on the website publisher to provide cryptographic proof of their content. For example, the NYTimes could create a digital signature of a photo and publish it on a blockchain or other trusted tamper-proof ledger as they publish the photo. Then anyone can verify that the photo is from the NYTimes and the date it was created.
He didn’t sell most of the drugs, he just provided a platform that allowed anyone to sell anything anonymously. Drug dealers used it because it was useful to them.
Drug dealers use private messaging apps like Signal as well. Should Signal be held responsible for drug deals facilitated by their app? (I know it’s not a perfect analogy, what he made was more blatant, but it’s an important distinction to make)