Yea that picture definitely reinforces the original Parks Service one. You can see all the empty space and people milling around, not that far in the background. The Obama inauguration was shoulder to shoulder standing room only.
They're using an increasingly popular derailment technique called the common ground fallacy.
The parent is asserting that the truth is merely a compromise between two different opinions, when in reality there's evidence enough to assert the truth, without making it a matter of 'right' or 'left' opinion. Their inability to provide their credible sources ("high def video") is because their opinion doesn't align with the reality of the situation.