Screen shots are important but can, of course, be faked: the Support team do not rely solely on the details reported via a ticket, but use it with other information, which is often why people aren't banned as quickly as many people would hope.
Mistakes can be made, of course, but there are follow up processes with the Support team and decisions can be reviewed. I would expect, however, that the percentage of fake reports is vanishingly small...
What if chess.com players made fake abusive comments that were actually never said by someone else and show it to chess.com staff and get them kicked?
Trust me it can be done to look legit.