Right, Tom. What that article did not explicitly say (or if it did, I missed it) is that the procedure was frequently followed using non-standard involute cutters that cut narrower tooth spaces than standard spur gear cutters. Frequently, certainly not always.
These special bevel gear cutters were typically sized to cut a face width between 1/8 and 1/3 of the full cone width. So the tooth right- and left-side profiles would be correct for a spur gear of the full cone diameter and the nominal pitch, but the width of the tooth would be appropriate for a spur gear of 2/3 of the full cone diameter. If the gear face is narrower than 1/8 the full cone diameter, you'd just use a standard spur gear cutter. These non-standard bevel gear cutters are marked just like spur gear cutters, with #1-8 and pitch, plus "Bevel" or some abbreviation thereof. They give better results than spur gear cutters for somewhat wider, but not arbitrary, bevel gear face widths.
Personally, if I were cutting one pair of bevel gears in my own shop, not equipped with anything more sophisticated than a dividing head for gear cutting, I would use the equal/parallel depth method.