Theres quite a lot of evidence, no proof I'd agree, but then there's no absolute proof I'm aware to the contrary either, so I don't know where you're getting this from.
The two pieces of evidence I'm aware of is that 1) Anthropic doesn't want their subsidised plans being used outside of CC, which would imply that the money their making off it isn't enough, and 2) last time I checked, API spending is capped at $5000 a month
Like I say, neither of these are proof, you can come up with reasonable arguments against them, but once again the same could be said for evidence on the contrary