GA pilot reported ATC clearance to cross intersecting runway with traffic converging resulted in stopping short and a critical ground conflict.

Narrative

Upon initial contact to ground which included current airport information and direction of VFR departure; I was instructed to taxi to the active runway with instructions to 'cross runway XX' which crosswind runway was along my taxi route.Approaching the intersection of the assigned taxiway and runway I was cleared to cross; I observed a single engine GA aircraft on the crosswind runway rapidly approaching the intersection. I applied brakes; and advised ground control that I was 'holding short runway XX for the (aircraft) on the roll.'Ground control advised in a terse tone 'we're working it out up here; and cleared to cross XX' in a way that seemed to imply it was inappropriate of me to stop and call.Coincidentally; I know the pilot and aircraft from the crosswind runway. I later confirmed that he saw me on his landing roll out and aggressively braked assuming that I may not stop.My ongoing consideration for improving safety of the NAS is in the way that situation was handled by ground control. The tone and message I inferred from ground control is that it was inappropriate of me to stop out of caution and speak up on frequency. In this case; both pilots stopping on the basis of 'see and avoid' despite ATC clearance averted a runway collision.My concern is exacerbated by knowledge that my students are nearly universally afraid to question/querey tower/ground control at this airport.