From what I've seen so far I'm wondering if maybe you guys are reading into the article something that really isn't there.
Tilly & his friend "Charlie" (as he called him) had a very specific difference here. According to the article, CBM believed that many par-5's should be reachable in two shots. Tilly didn't he believed that most par-5's should be true three-shotters, hence the reference to the article that Tom Paul made. It can be found in the October 1918 issue of Golf Illustrated in the Our Green Committee section and it does indeed include an illustration of a three-shotter with a "great hazard" in it.
Tilly, though, deesigned a number of wonderful short par-5's that he expected the accomplished player to be able to get home in two if he made two perfectly executed shots and these designs purposefully rewarded him for doing so. A good example of this is the 12th hole at Winged Foot West. When it opened for play it was 487 yards from the back tees and played at that distance during the 1929 U.S. Open. He tempted and challenged players to go at it in two and yet if they missed they would be severely punished as apr was definitely gone and bogey would be a very good score. Both Al Espinoza and Bobby Jones went for this green in 2 shots during their 36-hole playoff for the Open championship.
The real disagreement though had more to do with length of the hole than ability to reach it in two shots. Note how Tiklly wrote that "In his opinion 480 yards under normal conditions furnished a good distance for a three-shot hole..." Whereas Tilly believed "I still remain unconvinced, 480 yards is litlle more than a two-shot distance and there are hundreds of golfers in America who would eat it up with with a drive and a long iron..."
It his discussion of bunker usage on three-shotters here that I find more signioficant. CBM, because of his view that par-5's should be reachable in two shots and so should be "open to the second shot of any prodicious hitter who might reach it." Tilly believed in limting the angle into the putting surface in a way that would allow him to require the accomplish player to choose how close to skirt the hazards between tee and green because the best angles would invariably be close by the hazards he placed there with the final entrance into the green from a spot that allowed the front portion, including the approach to be used in his choice of shots while if he hadn't placed his second shot in the preferred location he would be forced to deal with the greenside bunkers.
Two very different approaches in philosophy yet both with their own inherent challenges...
By the way, Tilly had already written and published several other articles about types of par-5's at this point including his April 1916 Golf Illustrated article titled "A Novel Type of Three-Shot Hole" (see below) I believe this is the very hole and article that they were having their "friendly" discussion about.