You could calculate the likelihood over a certain distribution, in your case 1%. But when you do that you find that the third coin has a higher likelihood of being a fair coin than the first coin. That one has a pretty big bend in it. The ones after have a less than 4% chance of being fair. But to the OP's point, seeing that the third coin is more likely to be fair than the flat one (and is past a 45 degree angle) I think their claim makes sense with pretty good bounds.

To be fair, a 1% bias would probably not be detected in a hundred trials. CI for Bernoulli is +/- z * sqrt(p * (1-p) / n), so for a 95% confidence interval smaller than a percentage point, we have

1.96 * sqrt(p * (1-p) / n) = 0.01

0.5^2 / n = (0.01/1.96)^2

n = (1.96/0.01 * 0.5)^2

Or about 9604. So you need roughly 10k trials to determine with 95% confidence a bias of 1%.

Even a fair coin has a 51/49 skew in a normal flip.

https://epubs.siam.org/doi/abs/10.1137/S0036144504446436?jou...

But bending/weighting won't change that.