Not entirely true.
The biggest "gotcha" is typing -- C++ is much more strongly typed than C is, and the preferred methods for solving this in C++ are simply not available in C. Namely, you can silently cast between types in C (particularly pointer types), but not in C++. And C++ highly recommends using the static_cast/reinterpret_cast/const_cast methods for resolving these issues.
More importantly, if you learn C++ syntax and mannerisms, you'll probably find it difficult to deal with C (some may say this is good; and I prefer C++ myself, but sometimes it just isn't an option, or you have to deal with legacy code that's in C and not C++). Again, the most likely issues you'll encounter are dealing with pointers (particularly char*'s and general array usage; in C++ using std::string and std::vector or other collections is simply better).
It's certainly possible to learn C++, and then learn the differences between C and C++ and be capable of programming in both. But the differences are far more than just skin deep.
