I have to echo the sentiment of Namesilo, it is really hard to say definitively given we don't know the exact circumstances but I can give a general reply.
We follow the UDRP process and generally if someone makes a claim against a domain on a gTLD we will refer them to that process. We do not act on court orders from courts outside of our jurisdiction, which is the Bahamas. If we get allegations of a domain theft, it is usually accompanied by a recent transfer, and we will lock the domain/s so that we can launch our own investigations. But this has nothing to do with the courts and is more to do with just making sure that we are protecting domain owner's assets and livelihoods.
It is a really tricky deal for Registrars to be honest and we don't like being in this situation as it is lose-lose. Depending on the legitimacy of the complainant, we occasionally do need to seek legal representation and defend ourselves in court because we are caught up in a claim and want to protect our customers. This is very expensive for us and we don't get any extra money for the domain, but we spend 10s of thousands on this a year, so as to not allow a precedent. It can also block us from getting further investment in our company as financial investors will do due diligence and discover open court proceedings through this process, then raise as a risk. It sucks for us.
In the Brent Oxley situation I would guess that we would have locked the domain for a couple of weeks whilst we investigated the issue, when we found that the claimant had no legitimacy and that there was little risk to us from a legal point of view, we would have removed the locks and told the complainant to take a hike. That said, they probably wouldn't have tried it on a company based in the Bahamas because they assume they won't have much luck.
Best of luck to the domain owner.