That’s not a “gotcha” question.
If someone tells you a subway ride in Boston is 85 cents and another person tells you, “No, I fact-checked that, it’s $2.90,” you aren’t going to say, “How do I know you’re not lying, too?” If you distrust that second person, you can look it up for yourself, and that settles it.
When you ask how it’s possible to know whether a fact-checker is telling the truth, either you are not asking that question in good faith, or else you don’t believe that there are such things as facts.
I have spent many hours personally checking some of Trump’s bizarre claims. Often there is no shred of truth to them. The Washington Post confirms this, and I am able to confirm what they have confirmed. By their calculation, he currently lying 20 times a day.