Note that the quote about Anthropic is about Anthropic's desire to be perceived as a company that values safety, not a direct claim that Anthropic actually is safe, or even that it desires to value safety.
You must have interpreted the final sentence "A careful look at the company's decision-making reveals that this commitment goes beyond words" very differently than I did, or else you're splitting hairs in making your distinction.
I read it as a commitment to keep this costly signal, beyond just words. If an amoral oil company wants to keep employees/customers who care about the environment, they might both say that they care about the environment AND do costly signals that indicate that they care about the environment (like replacing plastic straws with inferior paper straws, even if it's annoying and costs money). This is different from the company actually caring about the environment. Maybe actually caring involves taking actions that matter more than paper straws. Which again is different from being good for the environment, overall.
I might be reading into the literal words too much though. I don't have a sense of how messages like that is read in political science academia and DC (the primary target audience).
At first sight, I also initially interpreted the use of the term "signals" or "signaling" the same as you interpreted it: with negative connotation that is often used for those who only care about the perception of the public, but not actually caring "by heart".
But after reading the first few pages in that document, especially with the comparison to Cuba missile crisis and the title "Decoding Intentions", it appears that the word "costly signals" here is about how to properly publicize our intentions, so as not to create misconception that may spiral out of control, like in the case of Cuba missile crisis, where unclear "signals" were given, causing a chain of misunderstanding to pile on top of another, making the situation worse.
The document seems to be a cautionary tale to prevent that kind of thing to happen again, this time with AI systems, especially when it's used in the military, where the consequences may be dire.
So, I interpreted the point of the document as (my wording):
Let us be aware on how we are communicating our intentions through our actions, lest miscommunications make chaos out of this rapidly advancing nascent technology breakthrough.