What you quoted says exactly that. The results differ by 450ppm from the constant even though the equipment used have experimental uncertainties of about 40ppm. The noise and non-gravity effects dominates the effect of gravity.
Maybe a graph will help. So here's a pie chart. Explanations to follow.

The entire circle represents the measured value. It's 1000000 ppm or a million parts per million. That's the same as saying 100%. It's the whole thing.
The blue area represents experimental uncertainties of 40ppm. 40 millionth of the measured value.
The red area represents an extra 450ppm difference due to noise and such. I've labeled it 'Circumstantial uncertainties'.
The green area, I would have preferred to keep unlabeled, but this particular tool doesn't allow that, so it's the lower value bound. What the true value is if the measured value has overestimated by the entire experimental and circumstantial error. The true value lies somewhere between this and the size of the whole circle plus the size of the uncertainties.
I think it's clear that, while the circumstantial uncertainties are much bigger than the experimental uncertainties, dominating them, perhaps, the entire uncertainty area far from dominates the circle.
Now, you might notice that neither uncertainties are actually visible. That's simply because the circle is much too small to show them. But I feel like this only emphasizes just how insignificant they are.