"I believe this is not the case because: XXX" would be a neutral response. And one that most people would give to most other strangers if they are meeting in real life. But on the internet it happens very often that people aren't actually as respectful as they would be in real life. And it happens very naturally too - I have close friends who have had insane arguments over chat apps which they would never have done in an eye to eye situation.

In general responding with a statement that assigns a quality to someone's work and effort is not appropriate. You can say "That information is not correct" if you want to be assertive but saying "You have not researched or read the correct information" is doing more then correcting information and becomes personal.

I've seen a lot of people, myself included have trouble with this distinction. But I have found it to be an important part of being "considerate" of others and being charismatic to them. People really react differently to the smallest of nuance in tone and wording regardless if they are adults. (I'd actually wager adults react much more strongly to that nuance due to having more experience to tell the nuances apart)