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.)
>I think we can all agree that SQLite does not fit that description
One of the reasons WebSQL died was due to how many memory bug related vulnerabilities SQLite had.
Bah waking up today to notice a typo, after the edit window. "And both C++ and Rust inherit some ... aspects" was of course meant to be "And both C++ and Zig inherit some ... aspects".