I find it bizarre that airport fire rescue equipment should be rolled and standing by at SFO for an incident that occurred in ABQ. You're right about no violation, however 14 CFR 91.13 prohibits "Careless & Reckless" operation of an aircraft.
That's terrific about the cameras allowing the PIC to inspect the belly of the airplane. HOWEVER, if he was so convinced that the landing gear was fine I fail to see the need to make a low approach of the SFO tower and have the gear inspected (especially if it was already inspected in ABQ). It creates additional workload for SFO ground to control all the fire department ground equipment on the movement areas, for tower to look especially closely at the landing gear and for Norcal approach resequence the aircraft back onto final.
I am absolutely not opposed to this. 14 CFR 91.3 allows the Pilot In Command of the aircraft to break any rule required to meet whatever emergency or situation they may have. If it was a choice between a crash or inconveniencing ATC, I would gladly be in favor of the latter.
The question I was raising is simply whether it could be interpreted as "careless" or "reckless" to fly an airplane several hours to your previously planned destination and meet your scheduling commitments when you don't have 100% confidence in the mechanical integrity of that airplane. Do you choose to land and solve the problem now or put it off until later?
If it were me, I would have landed at ABQ and gotten the airplane checked out on field. If I didn't, I would file an ASRS report explaining why I continued to the destination (should someone interpret my actions as violating 91.13, even if I personally felt they were justified). That might not make me an employer's favorite pilot, but oh well. Ultimately this ended up being a non-event and the PIC made a judgment call to continue and that was his decision to make.
Take the plane to where it can be fixed? Not that uncommon.
In 1975 I saw a C5A that had two fire warning lights. They decided to take the airplane to where it could be fixed as opposed to landing in Kansas City. The crew survived, the plane and the runway didn't.
The only FBO on field, Signature Flight Support, is horrendously expensive and would probably not be a company's first choice for Gulfstream maintenance especially if closer alternatives existed. However assuming this was the case...
I have a counter-example for you, although it's not fair to compare it to the above post since the Gulfstream pilot's judgment wasn't necessarily unsound.
Earlier this year an F/A-18 Hornet pilot departed an aircraft carrier in the pacific ocean inbound to Mirimar MCAS in San Diego. The airplane experienced fuel crossfeed problems that were a known serious event, but the pilot elected to continue to Mirimar and fly over a densely populated city when North Island NAS would do (both airports had maintenance, just because one happened to belong to a different branch of the military didn't mean it would have been impossible to fix the airplane there). The hornet then experienced dual engine flame out and landed on a house, killing an entire family, while the pilot ejected to safety.
Prematurely terminating a flight certainly isn't always the answer either, but the above example should illustrate just how wrong this invulnerability "It can't/won't happen to me" attitude can really negatively influence a pilot's decision making when a more serious emergency exists, with disastrous results (see Aeronautical Decision Making (ADM) attitudes as described by the FAA for further info).