Air carrier Captain reported they did not give way to another taxiing aircraft as instructed by ATC. Captain stated the crew was performing a checklist when their taxi clearance was issued and another aircraft may have mistakenly taken the clearance which went uncorrected by ATC.

Narrative

After being given taxi clearance of Kilo; Bravo; Charlie cross 22R and hold short 22L" we began to move. After turning onto Bravo northbound we ran the before takeoff checklist. As we approached the intersection of Bravo and Charlie; we noticed another aircraft approaching the same intersection from the opposite direction. We came to a stop and inquired about the aircraft and their intentions with Boston Ground. The controller replied with "That's Aircraft Y I asked you to give way to; but since you're already there go ahead and make the turn onto Charlie and cross 22R." We discussed this and believe that Boston Ground called for us to give way in the midst of constant comms on freq and while we were running our checklist; so we missed it. There was another Company flight on freq; and it is possible that they answered that call mistakenly and ATC did not catch the discrepancy.Cause: Busy radio environment while running a checklist led to us not hearing. ATC received a response from a different aircraft leading them to believe their instructions had been received when in reality they had not.Suggestions: CPDLC usage for ground ops; or additional ground freqs with fewer aircraft trying to talk to the same very busy controller."