These are strong and unsubstantiated claims.
The main competitions US labs are facing, are from one another at this point, not from open weight models. If anything, the competition from new entrants in the west (Meta, xAI, even Google if you think about it) has pushed things even faster, but regardless, I don’t see how OpenAI and Anthropic would have been any slower if there were no open weight models.
In my opinion it is the open weights that are pushing as much in tandem. Without them it would be easier between the top labs. They must have a large enough gap between OW to justify that extra cost. A business owner may prefer to be happy with 8/10 AI output rather than spend 5x more for that extra 2 points