So, I take two issues with pretty much all the deterministic assertions I've seen (those based on psychology - I don't deal in religious claims). Firstly, the research is largely based around things like the finger movement (which Peterson discusses in one of those videos) and the activation potentials. The problem is, we're not quite sure we know for certain what's going on in those measurements. They seem to be measuring something directly related to the decision, but what, precisely. Perhaps we're measuring the brain's process that leads to the decision. That leads to the second issue (which some would argue is philosophical, but early-stage psychology tends to be philosophical until we find a way to measure it): where does "choice" start and end? Is the "self", the mind, only confined to conscious awareness? Or if we train our brain to be able to make a decision unconsciously, does that decision count, too? Is there a part of the un-conscious brain that is still part of "self" (as opposed to being mere programming we respond to)? This is something we don't have a good model to handle yet, so any strong claims made either way, in my opinion, are ill-grounded.
We experience free will, but some measurements don't support that experience. Perhaps the issue is that some of what we experience lags behind the actual mental process we're experiencing. In other words, maybe we make a choice, but don't experience the actual choice in real time. Or maybe those action potentials are pre-programming we have no choice but to respond to. Or maybe those action potentials are the less-than-conscious "self" making the choice our conscious self will later experience. Or maybe those measurements aren't what we think they are. I don't think we can actually rule out any of those possibilities with current knowledge - and there are probably others I'm not aware of (some of which probably haven't been codified yet).