You’re correct that this is the broad definition, but GP is correct that that is a very common form of regulatory capture in the US.
In the case of OpenAI, were I to guess, they'll likely do things like push for stronger copyright laws or laws against web scraping. Things that look harmless but ultimately will squash new competitors in the AI market. Now that they already have a bunch of the data to train their models, they'll be happy to make it a little harder for them to get new data if it means they don't have to compete.