CAPT OF AN LGT ACR ACFT FAILED TO HOLD SHORT OF THE PARALLEL RWY AFTER LNDG ON THE OTHER PARALLEL RWY.

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ON AND DURING LNDG ROLLOUT ON RWY 28R AT SFO; FLT ATTENDANT IN CHARGE POUNDED ON COCKPIT DOOR DECLARING AN IMMEDIATE NEED FOR MEDICAL DOCTOR TO AID A PAX. THE FO WAS OCCUPIED WITH THIS PROB AS WE TURNED ONTO THE HIGH SPD EXIT (T) AND I ACKNOWLEDGED A XMISSION FROM TWR THOUGHT TO CLR US ACROSS RWY 28L. THE CONFUSION AND EXTRANEOUS CONVERSATION DISTRACTED BY ATTN AND MY FIRST NOTICE OF SOMETHING AMISS WAS AS WE WERE ENTERING RWY 28L WHEN I SAW AN MLG ACFT MOVING QUITE SLOWLY TOWARDS US. SIMULTANEOUSLY THE TWR BEGAN TO INQUIRE ABOUT OUR UNDERSTANDING OF THE CLRNC. SUPPLEMENTAL INFO FROM ACN 244404: DURING THE APCH; AT APPROX 2500 FT AGL; THE FLT ATTENDANT CALLED THE COCKPIT. CALL WAS IGNORED DUE TO STERILE COCKPIT PROCS. FLT ATTENDANT AGAIN CALLED THE COCKPIT AND KNOCKED ON THE DOOR AND WAS ADMITTED TO THE COCKPIT. SHE ADVISED THE PLTS OF THE IMMEDIATE NEED FOR A DOCTOR DUE TO A MEDICAL EMER. THE FO WAS DISCUSSING THE SEVERITY OF THE PROB WITH THE A-LINE FLT ATTENDANT. DURING THIS DISCUSSION THE CAPT ACKNOWLEDGED THE TWR TAXI INSTRUCTIONS. THERE WAS CONFUSION AS TO TAXI INSTRUCTIONS ISSUED. FO HEARD HOLD SHORT AND THE CAPT THOUGHT HE HEARD CLRED TO CROSS. BOTH PLTS WERE DISTRACTED BECAUSE OF THE DISCUSSION ABOUT THE MEDICAL EMER. CAPT CALLED THE TWR UPON ARR AT OPS TO DISCUSS THE PROB. TWR SAID THAT NO FURTHER ACTION WAS TO BE TAKEN CONCERNING THE RWY INCURSION. THE MEDICAL EMER WAS FOUND TO BE VERY MINOR AND WAS HANDLED BY THE GATE AGENT.