RAT 5 - the answer is YES. The little box is smarter than you thought!
AVIATORPK - A TCAS RA is based upon you managing a minimum 1500ft/min during any aviodance manouevre..... this is often not possible in even a A340/B747 with an engine out.
By switching to TA you are telling the box (and any other acft) that you cannot meet the required performance for a RA.
To answer the original question: San Francisco requires TA as the parallel approaches are so close.