No, that's provably false by a fairly simple existence proof. If it was true that using C results in an "extremely high amount of crashes/memory bugs", we would expect to not find any substantial pieces of software written in C without an "extremely high amount of crashes/memory bugs". Now where exactly you draw that line is necessarily going to be somewhat arbitrary, but by any definition, I think we can all agree that SQLite does not fit that description. Yet SQLite is written in C. Therefore, we conclude that the statement must be false. QED.

Now C does have some aspects which make it more prone to crashes and memory bugs. The less strong statement of "using C results in a higher propensity for crashes/memory bugs than Rust" is absolutely true, I would argue. And both C++ and Rust inherit some (but not all, and not the same) of the aspects which make C prone to memory bugs. (So does Go, I would argue, but less than C++ and Zig.)