Outside of the club's colloquial use of "foursome", their policy is not breaking any rules.
The USGA's take on priority on the course begins with
"Unless otherwise determined by the Committee", and it seems that four players in a group is the "determination" arrived at by the committee.
The second USGA concern is that
"priority on the course is determined by a group’s pace of play". The club has made the determination that four players is their 'standard', but they are still in 'compliance' with what the USGA wrote because they allow for the four player group (their 'standard' as determined by the committee),
"to let groups of lesser number play through at their sole discretion, based upon overall course traffic and pace of play", which aligns with the USGA's own request that
"priority on the course is determined by a group’s pace of play". It may not be the most likeable policy, but it's fully in-bounds.