Look, we don't know for sure what happened at that conference. We have two very different stories on what went down. Neither story can be verified and we cannot even prove that the sources of one or both of the stories aren't biased. The Institute knows that they had nothing to do with the failure at that conference and the Commonwealth at large knows that the Institute shot the place up. The source of this document of yours is going to need to be from a party that both sides trust and at the beginning nobody is in a very trusting mood.
It isn't just the supposed massacre of the CPG delegates this document is going to have to explain away, either. There is the kidnappings and assassinations of Commonwealth residents. The synth infiltration units the Institute has sent out and all those super mutants the Institute created. Now currently nobody outside the Institute knows about its connection to the Commonwealth super mutants, but if they start working with outsiders again, word will eventually leak out.
As for the Brotherhood, They are there to destroy the Institute. If the entire Commonwealth wants to ally itself with the Institute they will feel the hammer. The Brotherhood may lose but win or lose the results will wind up being the most bloody and least peaceful resolution.