Electrically, it is not really that dissimilar in configuration from having four grounding rods at the main service--it's just that two of those rods have 150ft between them and the main panel and don't have 150ft between them and the sub-panel.
That is about grounding for human safety. Grounding to protect appliances from surges involves additional factors including equipotential, conductivity, and impedance.
If a building is 150 feet away (and not properly earthed for surge protection), then it can even act like a lightning rod connected to appliances in a main building. When a connection between structures is that far apart, then each end must connect to a single point earth ground where it enters that structure. Connected directly and low impedance (ie less than 10 feet) with a hardwire or via a 'whole house' protector.
What happens when lightning strikes AC wires far down the street? That current may be hunting for earthborne charges miles beyond a secondary building. Best path is incoming to the main building, into a secondary building via that 150 foot buried electric cable, into a stereo, and then outgoing to earth via speaker wires. Does not matter if a stereo is on or off (that should be obvious).
Damage is often on an outgoing path (ie speakers). Many who conclude only from observation would then wildly speculate a surge was incoming on speakers.
Obviously protection means connecting any destructive surge to earth BEFORE it could enter any building. That means single point earth ground for each building. Earthing that both meets code and exceeds code requirements (ie low impedance). Every wire inside any incoming cable must connect low impedance to that single point earth ground BEFORE entering.
None of this is new. Protection was routinely implemented this way over 100 years ago. Protection is about how a current gets to earth - and where hundreds of thousands of joules harmlessly dissipate.
If buildings are 150 feet apart and both do not have their own single point earth ground, then appliances in both buildings are at serious risk from an anomaly that might occur once every seven years (obviously more frequently in FL).