Back then the compilers sucked. They would take complete crap of code and still it would work. They were like browsers are today. (from my experience from going through one old MUD code)
Today the song is different. Not only will the compilers warn you of many things, there's even tools for static analysis (and dynamic). So the argument that C (and even the more complex C++) is inherently insecure holds much less weight (just go run old code through a static analyzer, or a normal compiler for that matter).
That said there's only one way to write a "secure program", and that is formal verification.
People that talk with a serious tone should back up their claims, at least that's my opinion.