Several undercover reporters have reported this. They are obviously lying. If the administration confirms the same, they are obviously lying. Who shall we believe then? The NYTimes?
What this reads as is a bunch of credulous X users trying to one-up each other and looking for reasons that Trump and his cronies are not once again lying to your face.
It is neither necessary nor particularly useful for them to be running plates for reasons you've already identified.
That's exactly what they have done - shared the information pointing to the organized attempt to interfere with the ongoing federal operation. This is a crime.
Physically obstructing them is interference. There are countless videos where protesters can clearly be seen to do this, even as they are then defended as supposedly "merely exercising free speech rights".