Well it’s likely because both sides have seen instances where something that is absolutely true be silenced with a “disinformation” or “false news” justification. In recent memory, it has been more “left supporting” news stories that have been silenced than “right supporting” ones that have been falsely silenced. But in recent memory:

• Joe Biden’s son’s laptop. Later confirmed to not be Russian and to be accurate.
• Various emails from the Clinton Campaign being leaked. Claimed to be faked but largely proven accurate at the time of the leak (via DKIM) and with future legal action.
• Several stories about Biden’s declining health. Some of these during the primary pissed of the Bernie wing of the party for being silenced, some during the general pissed off Trump supporters. Biden is 80 years old. Everyone 80 years old has declining health but discussion of it was generally verboten.
• “Lab Leak Hypothesis” Still not proven true or false but believable enough that several government agencies believe it to be credible.
• Origins of the “Russia Collision” story being a person affiliated with Clinton/DNC.

And there’s a long list of obviously biased “fact checkers” making obvious mistakes. Like claiming Romney was lieing when he accurately predicted the outcome of Obamacare a claim that they would call the lie of the year on behalf Obama for repeating in 2013. I pick on polifact for being left leaning but there’s similar right wing “fact checkers” doing similarly biased fact checks.