This is lack of judgement and you should take it as a life lesson. You gave a reference with whom you had a bad experience and did not get a confirmation that would support you in this situation…

I don't think you can salvage this, of course you can try. You can go for the “I give you 3 months on experience for free, if you don't like me you can just send me away and it costs you nothing”.

Dear Anonymous A,

Am I understanding you correctly? A Consulting firm offered you a ‘conditional’ offer and that: 

1) this ‘conditional’ offer was contingent upon submission of 2 professional references not initially included in the application process; 
2) these professional references would come from a source which your aspirational firm KNOWS FOR A FACT is a)  - a competitor firm and b) a firm at which you still work but are intending to leave imminently;
3) the contents of 1 of these professional references was, in your own words, “not sufficiently good” (which, I must say, is rather unusual wording) and that your aspirational firm reverted to you with this assessment of the reference;
4) these assessment of the reference caused the firm to renege on its ‘conditional’ offer to you

Am I understanding all this correctly?

If I have misunderstood you, could you clarify what I may have missed?
If indeed I have understood you correctly, I would say that the situation is too bizarre, too unlikely, too amateurish for a professional organisation, and too exposed to civil liability to be true.

In any case, Pedro is right when he recommends you to consider this a life lesson because either way, you learnt something important.

(editiert)

Super unprofessional by the Tier-2 boutique. And a warning signal! They are actually admitting that they have zero trust in their own ability to assess candidates and will rescind offers after having talked to a third person who they don't even know. 

Please move on and get maximum distance between yourself and that company!

Cheers, Sidi