He's just a little out of date. At the dawn of the Regency, frock coats nearly disappeared, with various forms of cutaway coat worn for both formal and informal dress. In the 1820s, the frock coat or redingote
(specifically a fitted, skirted coat) began to move in as a cutaway-coat substitute. At first it sometimes is worn open in the front, in line with the cutaway styles. The '30s have plenty of redingotes. As styles became less closely fitted moving into the '40s, it more closely resembles what the midcentury wearer would recognize as a frock coat.
You are right that the cutaway gradually became fossilized as the formal
Early redingotes (1829): http://regencyfashion.org/pc/pc641.htmlhttp://regencyfashion.org/pc/pc655.html
1830 morning dress, showing both cutaway and frock-type coats:http://i201.photobucket.com/albums/aa284/Satorarepo/MorningDresses.jpg
1830 frock coat (left), and military coat (blue), both also identified as morning coats:http://i201.photobucket.com/albums/aa284/Satorarepo/morning1830.jpg
1840 cutaway and frock coats, note frocks still worn open:http://www.fashion-era.com/images/1800_1900_laver/1840_laver_men.jpg
1845 frock coat worn buttoned, beginning to take on the more relaxed shape:http://4.bp.blogspot.com/_fKdqCtATOSo/TDxODDk13cI/AAAAAAAAG6Y/lT8wWWksXp4/s1600/1845+fashion+plate+of+outdoors+clothing+styles+for+women,+men,+and+girls.jpg