Fact checking is not objective, you just need to convince someone that your facts jive with their perception.
Once solid evidence is in sight then are usually some clean objective takes to be had and some fairly obvious or likely subjective takes that a reasonable viewer might have.
The real problems happen when one side objects to what counts as evidence at all or one side puts forward low quality evidence and claims it is beyond reproach.
Assuming one's evidence is subjective, and one's judgment of it, and some other things.
> than appealing to vibes or appealing to baseless authority.
"Baseful" authorities are not necessarily objective. In fact, we have massive amounts of evidence that they are very often not.
Different people disagree for different reasons. But only the most deranged disagree that what they can do and effect is worse evidence than some authority. So things like "trying it for yourself" have worked consistently as evidence for most of history. Today "it" can be a bunch of different categories of experiments and experiences.
Even then lots of experiments are out of reach of most people, sometimes financially, sometimes intellectually. Some people think essential oils helped their cold go away in 3~5 days when most colds go away on their own in 3~5 days and. So there needs to be some delegation of authority. This is where a lot of problems leak it. Some people grant authority to some for silly reasons (like an a priori assumption they can do no wrong) other for good reasons (like lots of experience working in a relevant field with many published papers).
For many people exploring the different levels of subjective evidence can get two people to understand why the other believes something goofy. This takes time, isn't guaranteed, but it can be done at least some of the time to show where evidence and many beliefs fall on a gradient of quality. This fails when people hold some belief as firmer than reality, like what conspiracy theorists or religious zealots do.
> To use an example nearer to my heart, say you want to compare how many Apple and Samsung devices were sold in the past five years. The service would locate and collate that information.
My question would be to what extent is this really a problem. Sounds like they're going to be competing with Google and Bloomberg which is a tough sell. Finding data quickly is their bread and butter.