From what I've read, that's already part of their training. They are scored based on each step of their reasoning and not just their solution. I don't know if it's still the case, but for the early reasoning models, the "reasoning" output was more of a GUI feature to entertain the user than an actual explanation of the steps being followed.
I work for state government. We've used the ACS survey to try and determine whether we were unfairly targeting non-native English speakers with some of our decisions. It's also used a lot in academia.
If I had to guess, commercial organizations have access to more invasive and higher quality data that they obtain through credit card companies, lexus-nexus or other data brokers. This attitude mostly harms organizations involved in the social sciences.
It sounds like they are describing a regex filter being applied to the model's beam search. LLMs generate the most probable words, but they are frequently tracking several candidate phrases at a time and revising their combined probability. It lets them self correct if a high probability word leads to a low probability phrase.
I think they are saying that if highest probability phrase fails the regex, the LLM is able to substitute the next most likely candidate.