No, there's not. At least, if there is, its not the one you claim.
> They want people to think either: 1- it will help me earn more (because I make less than the BI) 2- it won't change anything for me (because I already make more than the BI)
Who is "they"?
> But obviously, these two assertions can't be true at the same time.
They can both be true if the benefits plus (reduced) admin costs from BI come strictly from the benefits plus (higher) admin costs of the welfare programs it is replacing. (There are people who make less, in the short term, in that scheme, but its only some subset of the people who are making money from the admin costs of the replaced programs.)
They can't if you set BI at a level that requires more money than that, or if you do it without replacing any existing programs, but neither of those is inherent in the concept of BI (and the latter, at least, I've never seen proposed.)
