> do you think they are just lying
Yes. They're constantly lying, and constantly getting caught for it. They have a reputation for it. Why do you think this would be any different?
Their standard opt-out agreement frames it as if they won't train on your data, but they do anyway, due to legal loopholes. They essentially clean-room everyone who opts-out, so while it's "technically" not training on "your" data, to the model it makes no difference. Your alpha and IP is not safe. Paying customers are now more easily able to clone your business as well, not just Anthropic themselves.
The only reason this hasn't leaked yet is fear. Anthropic is a very litigious and dangerous company. Only a matter of time though, someone there will grow a spine and speak up.