Company presence at an airport should not be part of the 'suitable' selection criteria for a diversion due to system failure requiring land at nearest suitable airport. For scheduled operations where a particular alternate is part of the planning process it is usual at least to have agreements in place with handling agents etc to cover the diversion case. However even if those arrangements are not in place - for the system failure case - the rest of the 'suitable' definitions like fuel, ground support, runway and taxiway strength etc apply in the decision-making process.
My reading of 'land as soon as possible' is just that - depending on the severity of the situation, the Captain must decide where to land even if it is not on an airport at all. Example being uncontrollable fire or severe smoke in cockpit could require ditching or off-airport. Lesser but still serious situations could be any runway where the aeroplane can be brought to a stop without incurring further risk to life and limb or airframe damage.