Larry Edsall in Automotive News goes into more detail here. According to most stories, including Edsall's, Earl reacted by claiming that body engineers altered his staff's design. He used this (along with his friendship with Alfred P. Sloan) to gain final sign-off on future designs from his Art & Colour section.
I am a bit skeptical. So far as I know, there is no visual evidence of the designs Art & Colour prepared for various Buick body types. If this is so, then the matter cannot be resolved. My guess is that Earl's design did have that bulge. Checking with the styling history bible, "A Century of Automotive Style" by Michael Lamm and David Holls, I notice on page 91 that former Chrysler Corporation stylist Jeff Godshall is of the same opinion. I base my case on the reasoning that body engineers, a conservative lot, would never think of making such a major departure from strong conventions of the time unless they were under instructions to do so.
We begin with four images of 1929 Buicks. The notorious bulge is along the belt line.
So yes, that Buick bulge was definitely out of the American car body design mainstream during the 1929 model year.