Consider me incredibly skeptical of any of these claims.
And the Deepseek one sounds even more dubious as Deepseek is one of the cheapest model around, why relay anything to a more expensive model? I'm sure even the gray market Claude prices are still higher than Deepseek.
There's also an argument to be made that paying the token full price may be cheaper than going through your one RLHF or whatever other techniques that costs money.