I haven't followed the story closely, but apparently Trump made exaggerated predictions or claims about the size of the crowd at his inauguration.
I haven't followed the story in detail because I avoid stories like that. I don't need to get embroiled in microscopic debates. I don't need to take sides on every controversy du jour.
It's a mistake for conservatives to get into the habit of defending Trump's statements. Trump is loose with the truth. That's a given. I expect him to make factually indefensible statements. That's a vice he shares in common with Hillary.
It's hardly surprising that the turnout was lower for Trump than Obama. DC is 50% black and 75% Democrat, so naturally there'd be higher turnout for the inauguration of a black president, or a Democrat president, not to mention both in one person. That's the obvious response to make, rather than making demonstrably false claims or foolhardily predictions. Aerial photography is hard to dispute.
But this is all a distraction. Now that he's president, it really doesn't matter so much what he says, but what he does. That's what we need to keep our eye on. Conservatives should resist getting caught up in the melodrama between Trump and the media. Focus on what Trump is doing, and Congress is doing. That's where the real action is.