I think far more interesting than that headline figure is the data they have given in Table 1. Of their 48 participants, 10 had the opposite result and showed a bias to the coin landing on the opposite side it started, and there were a handful of participants with a very severe bias, with one showing a bias of 60/40. So they key take away I think is not "51/49 bias of the same side you started with", but rather "everyone has their own individual bias when flipping a coin".

Given that, and given that each coin itself will also have its own intrinsic bias, then again the solution is the simple one I've outlined many times before - use a von Neumann debiasing approach, but also start each flip from the same position (i.e. heads face up). That way any bias in either the coin or your technique is completely eliminated and you will always end up with a complete random result.