Earlier quoted context omitted.
I think the issue is not their security team, who seem to do quite a good job securing iOS (which I'd consider one of, if not the most, secure consumer operating systems out there). The issue is that securing an OS is hard . It's hard to make it that someone with physical access to the device cannot just run code on it, which is what jailbreaking (in its purest form, on iOS devices) is.
Arbitrary code execution is different than requiring physical access to the device. The JailbreakMe site could have run malicious code and it could have spread itself and run without the user knowing.
Also, even if JailbreakMe was malicious (or somebody used the same code or exploits in a malicious way), it could not "spread itself": it was a browser exploit (although it would be possible to run without the user knowing).