Air taxi Captain reported during departure taxi another aircraft taxied toward them at a high rate of speed and did not give way as instructed by ATC. The Captain applied brakes firmly to avoid a collision.

Narrative

We were cleared to taxi via Charlie to cross 4L and hold short of 4R. This took us across Taxiway Bravo. We were taxiing at a slow rate and conducting the before take off checklist and run up flow. Aircraft Y taxied towards us on Bravo at a high rate of speed. They had not been mentioned in our clearance. I hit the brakes. My First Officer asked the Controller which aircraft was meant to give way; and the Controller indicated that Aircraft Y was supposed to have given way to us. Since we had come to a complete stop; and to ensure our safety; we gave way to them. The Controller apologized. I believe he may have not believed we would be near each other since we were taxiing slowly and conducting a checklist; while Aircraft Y was taxiing quickly. As Aircraft Y was using a medevac call sign; he may have assumed we were giving way to him. I believe the Controller may have thought there was no chance we would approach the Bravo/Charlie intersection at the same time. He may have been over tasked as well. I did not hear Aircraft Y's clearance; I don't know if 'give way to Aircraft X' was mentioned. In this case having two pilots and taxiing slowly helped to prevent a near miss. The taxi is a very high workload time; as Boston is busy and the run up; brief and checklists must be executed while maintaining a look out.