Jeff,
Note when Tilly makes that particular comment he refers to the architect who is also "the conscientious builder..." Yes, where the architect is also the builder, 11th hour changes could be expected that he would see as necessary from what his model portrayed. Tilly, though, really was anal about his models and tried to create ones that depicted what should be there and never deviated from.
Tilly actually sold plans for greens that also included actual models, including contours, as a separate form of design service. He did these by having having topos sent to him with the routing in place and then produced them. How many did he do? No one knows, nor is there even a single course that professes to have "Tillinghast-purhcased greens" that we know of. Still, some must have been sold and built because he advertised this service for several years...
Another thing to remember is following the above statement Tilly chided those who criticized the professional player who also designed courses for the quality of their work. He pointed out how they couldn't be reasonably expected to be on site for the long periods of time needed to do so to produce a championship-quality course. In this I believe he was more marketing his work than being kind to fellow members of his craft. He was basically saying, I'll be on site and you'll get a great course whereas those others won't and you won't get a good course...
To finally answer the question, tilly preferred making his models on site for the very reason mentioned above. In doing so he knew that fewer 11th hour changes would be necessary or happen. He also knew that by leaving these for the builders to refer to that what he envisioned would have the greatest chance to become a reality.
By the way, the large model of Bethpage State Park showing all four courses in place may very well have been done by Tilly... It was kept at Bethpage for the entire project and oft times referred to when questions arose in the building process. How long it remained on site and where it is today is a mystery...