Yeah, but that's not why people are upset about factchecks. They're upset about it being used in nitpicky ways in an attempt to score political points, eg. https://x.com/NBCNews/status/785299709342654465
This is also why I wish political slogans were better worded. Yes it's catchy but others dismiss it at face value when there is perhaps some truth to whatever nuanced grievance they're trying to express. Further polarising debate.
Or when they "fact check" a statement with 4 paragraphs of text that amount to "it's true but inconvenient so we'll say it's been 'fact checked' to undermine the statement."