I don't know how Frank presented the old Mothers, since I never read the book. There might be some opinions on what he said, but I - or anyone else - could not make any corrections to anything Frank did.

Jimmy Carl Black on Frank Zappa:

In the seventies he toured with Captain Beefheart & the Magic Band and with Geronimo Black the band he founded with Mothers wind player Bunk Gardner. Band chronology
The Keys (1962 - ?)
The Soul Giants (1964)
The Mothers of Invention (with Frank Zappa 1964–1969)
Geronimo Black (1970–1973)
The Mesilla Valley Loboys (mid/late 1970s)
The Grandmothers (1980 onwards)
Jimmy Carl Black and the Mannish Boys (1987)
Brown Black & Blue with Arthur Brown (1988)
The Jack & Jim Show (with Eugene Chadbourne 1991–1994 2007)
The Farrell and Black Band (1995 onwards)
The Muffin Men (1992 onwards)
Sandro Oliva & the Blue Pampurio's (1996 onwards)
Jon Larsen's Strange News From Mars Band (2006–2008)


Discography


Solo
Clearly Classic (1981)
A Lil' Dab'l Do Ya (1987) − as Jimmy Carl Black & Mannish Boys
When Do We Get Paid? (1998)
Drummin' the Blues (2001)
Is Singin' the Blues (2002)
Hamburger Midnight (2002) − as BEP (Jimmy Carl Black Roy Estrada and Mike Pini)
Mercedes Benz (2003) − as Jimmy Carl Black & the X-Tra Combo
Indian Rock Songs from Jimmy Carl Black (2005) − live album
How Blue Can You Get? (2006)
Where's the $%&#@ Beer? (2008)
I Just Got in from Texas (2008) − as Chris Holzhaus Jimmy Carl Black & Louis Terrazas
Can I Borrow a Couple of Bucks Until the End of the Week? (2008)
I'm Not Living Very Extravagantly I'll Tell You for Sure. Jimmy Carl Black (February 1 1938 – November 1 2008) born James Carl Inkanish Jr.

was a drummer and vocalist for The Mothers of Invention.