Every professional security researcher reading this just raised an eyebrow and thought to themselves, "That's a vulnerable application." In fact, your team (or a similar one at AOL) did introduce vulnerabilities[1][2]. If we assume that, as you imply, AOL really was exclusively composed of above average C developers writing high quality code, this should really just demonstrate the point for us.
I'm sure your team wrote high quality C code (or at the very least, tried very hard to write high quality C code), and as someone who likes C I also dislike the meme that C should simply not be written, no exceptions. I'd probably change it to, "Don't write C unless you need extreme performance, have great engineering resources and you'll generate unmitigated financial returns such to make any reasonable business risk assessment moot." That means virtually the same thing for anyone reading it, but it sounds a lot less sexy and memorable as far as programming aphorisms go.
I have never professionally audited a C project and not found a vulnerability. Most of my friends in this industry would likely say the same. I've never seen a serious audit of a "large" (100kloc or more) C project by a serious, reputable firm with no vulnerabilities reported. If you wrote 2 million lines of C code, if you wrote libraries from scratch, you have serious vulnerabilities. Otherwise, your engineering practices and resources exceed NASA's in formal verification and correctness.
I believe it is theoretically possible to write 100% safe C code, for some approximation of that ideal that leaves aside the ivory tower definition ("the only safe machine is the one which is off"). But I also believe this is so expensive and resource intensive (secure coding standards, audits, attempts at formal verification and provable correctness) that it's just generally not realistic in practice.
The reason I am saying all of this is not to attack you or your sense of worth as a C developer. Rather, I'd like you to consider that you simply have no idea how many vulnerabilities exist in ICQ. In fact, I found eight different security reports for ICQ, linked at the bottom. One of the more serious ones allowed arbitrary email retrieval, which I'm willing to bet was introduced because your team liked to develop in-house libraries and decided to do that for POP3.
C is a language which is both very powerful and which requires constant vigilance while coding. It is a language which makes pushing a buffer overflow to production on a Friday at 3 pm very easy. I bet your team was comparatively well-versed in C vulnerabilities for the time, but the very fact that you rolled libraries from scratch tells me you already have a high probability of errors showing up. Rolling a library/framework in-house is basically the first thing security researchers look for in an audit, because the third party ones are (usually) more secure due to their exposure. When you further consider the probability of third party software you did use becoming vulnerable in the future, changing compiler optimizations introducing new vulnerabilities and the sheer size of the SEI CERT Secure Coding Standard itself, you are left with a very dangerous risk profile.
We cannot expect C to be a safe language for general use if you need to have the rigor of one of the best research organizations in the world coupled with the top 0.01% of all C programmers. It just isn't feasible.
[1]: http://www.coresecurity.com/content/bevy-of-new-icq-vulnerab...
[2]: https://www.cvedetails.com/vulnerability-list/vendor_id-123/...