It's marketing. Microsoft certainly didn't want to admit that "Hey, we're making Java 1.1!"
First, it would be the same as admitting that Java is actually worth copying, which is a bad move if you're trying to beat Java.
And second, it would scare off all the native C++ developers who got scared off by Java's clumsiness and early performance problems.
So they say that they're building on C++ and everyone's happier.
In reality, of course, nothing could be further from the truth.
If C# and Java have a common ancestor, it is not C++, but "C with classes"; specifically, the very earliest versions of C++, long before it was standardized, and before most of what makes it useful today was added.
It was little more than an attempt at bolting some OOP functionality onto C.
C++, since then, has gone in a completely different direction, letting go of the OOP obsession, and exploring a much more functional style, using a compile-time form of duck-typing to create generic programming. Some incredibly powerful and elegant libraries have been added to the language. None of that is at all represented in Java or C#.
C# is definitely inspired by Java more than anything. And where it is inspired by C++, it is inspired by this early "C with classes" variant, rather than anything resembling modern C++.
But C++ was, and is, considered a "cool" language by many. Microsoft wanted to tap into that "cool" and bring it to .NET.
Personally, I'd consider C++, C# and Java to be siblings. They're all derived from the same "C with classes" protolanguage. C# and Java took a less direct route from there than C++ did, but it's still where most of their inspiration came from. That's where they inherited the weird notion of OOP that has virtually nothing to do with what Alan Kay/Smalltalk proposed, and it's where they inherited the clumsy C-like syntax.
It's a bit like saying that we humans are evolved from apes. We're not. We just have a common ancestor, and that common ancestor was somewhat ape-like. C# isn't derived from C++, they just have a common ancestor that was slightly C++-like.