I had the same recollection as you, but just looked through a Turbo C book I have here and couldn't find any reference to its big brother. A bit of Googling later, and it turns out Borland C++ was Turbo C/C++'s successor. The releases went like this: Turbo C 1.0, 1.5, 2.0, Turbo C++ 1.0, Borland C++ 2.0, then onwards. So Keen may require features that only appeared in 1991 onward.
Microsoft took more of the approach I think we're remembering. For example, BASIC PDS 7.x being the more professional version of QuickBasic 4.5.
So then where does Turbo C++ 3.0 fit in? My copy is (C) 1992, but it was still being sold in 1999, alongside what I'm pretty sure I remember as Turbo C++ 4.5 that targeted versions of Windows that were not out in 1991...
Boy, remembering that really digs up some nostalgia...
edit: I see the "Borland C++" wikipedia page present it as the successor, but the "Turbo C++" wikipedia page describes it as the hobbyist counterpart. The release dates and version numbers line up really well, so that makes sense. I was a hobbyist at the time.
Hmm, weird, I don't know. I only got as far as Turbo C 2.0 and then jumped ship to Turbo Pascal for the next several years (I know, I know.. not a great decision in hindsight!) ;-)
The Turbo/Borland distinction was present for both C and Pascal products from Borland all the way up to Turbo/Borland C++ 4.5 and Turbo/Borland Pascal 7.0.
For instance (different language but same company), Turbo Pascal 7.0 and Borland Pascal 7.0 co-existed at the same time. They were simply targeting different markets. I vaguely remember the same thing about Turbo C++ and Borland C++...
Microsoft took more of the approach I think we're remembering. For example, BASIC PDS 7.x being the more professional version of QuickBasic 4.5.