SHP is definitely not a public school as it's probably the most affluent with arguably the most beautiful and spacious campus in the Bay Area. The times the Gators did play the Privates, they have done very well defeating Bellarmine twice for CCS Open titles, Riordan for CCS D3 and beat SI and SHC last season in the CCS Sectionals. This tiny school has dominated in aquatics (primarily Water Polo).
The SHP campus in hyper-pricey Atherton (where a Port-a-Potty can set you back a month's pay) is so spacious it includes a graveyard. It's a cemetery for deceased nuns of the Order of the Sacred Heart. It's located not far from the football field. SI, take note.