I believe the theory is that the A players, secure in their own skills, want to be able to delegate work to people who are as competent as they are, whereas the B players want to surround themselves with people who make them look good by comparison.

A prospective hire who is an A (in whatever field) wants to work with their kind, and so is less likely to sign up at a company full of B-level people.

Also, as mentioned above, it is harder for many B-level people to recognize and value an A level person in the hiring process. An A may come across as arrogant by describing things as good or bad to a B when they're simply knowledgeable and confident because of that.

And by that mechanism, C players use the "only hire A players" rule to claim that A players are "not good enough", though such objections don't get raised about other C players.

There were some A programmers at Amazon, and they were respected, but they weren't the ones who made the hiring decisions. Since any B or C can veto any hire, A people often didn't get hired in favor of B or C people. (and A people who already worked there, eventually, got excluded from hiring loops because they're "needed elsewhere.")

what prevents A players from hiring B and C players They know it will not end up good for anybody. Also they understand hiring another A player or if possible an A++ player is good for overall health of the company.

prevents B players from hiring A players Ego and in a big corporation, the fear of the hire going ahead of you.

Also another deadly combination is the B player who hires another A player thinking they themselves are A+ player and spoils the fun for everybody.

proponents of the mantra would say that this means you're an "A" player.

there is some research that shows that your own competence directly affects how good a judge you are of your/others relative competence, i.e. people who are low competence will rate themselves routinely as 9-10 / 10 but people who are high competence will rate themselves 5-6 / 10 ...

If A players surround themselves with A players and B players surround themselves with C players then those numbers sound about right.