I take exception to the sign where it states, "Belmont is one of two-and the first-public Tillinghast courses to have hosted a major championship, joining Bethpage Black."
Belmont never hosted a major championship. The 1949 PGA championship was contested on the Tillinghast-designed golf course at the Hermitage Country Club which would later become the public course known as the Belmont golf course.
I appreciate the nit-picking, but if you rename a course, it retains the history. Belmont (then Hermitage) hosted a major. Hermitage still exists… at a different place and with different golf courses, but they can't claim to have hosted the major at those courses, even though they kept the name.
Was Hermitage public in 1949? If not, then your second point applies to them as well.
If one wants to say that I'm nitpicking, then the sign is still incorrect in two ways. Cedar Crest Country Club was the site of the 1927 PGA Championship which was contested on its Tillinghast-golf course. Years later it would become, and still is, the Cedar Crest Golf Course, one of the city of Dallas, Texas municipal courses, making IT the first public Tillinghast golf course to host a major championship and that there have been 3 major championships held on Tillinghast public golf courses.
Cedar Crest wasn't public when it hosted the major, was it? If it wasn't public at the time but later became public, that doesn't count in my book.