The answer is: yes, OpenVZ stable kernel is secure enough to be used for production workloads and in hostile environments. Why? The long answer involves a comparison of different virtualization techniques and their SPOFs, a description of OpenVZ architecture, the "denied by default" principle, the fact that its practically proven on a thousands of servers, etc. The short answer is: because we care.
Security is quite a complex field. It's not enough to write secure code once, or secure your system once. In the real world, security comes from constant care. In other words, it’s not enough for a sys admin who is using a good, secure operating system, but doesn't care daily about security.
The Linux kernel is quite secure. Still, new problems are found and resolved from time to time, by those people who care. Most of them are security experts (like Solar Designer), others just work on Linux.
A few days ago, Red Hat released a new update to RHEL4 kernel (RHSA-2007-0014). Let me quote: Red Hat would like to thank Dmitriy Monakhov and Konstantin Khorenko for reporting issues fixed in this erratum.
Both Dmitriy and Konstantin are working in our Virtuozzo/OpenVZ team. Dmitriy works in the Quality Assurance department (which I wrote about before), making sure our kernels are rock-solid (by trying to break it badly, that is). Konstantin works in our kernel support team, mostly fixing the causes of kernel oopses. Besides that, as you see, they both care for security (as well as everybody else in our team). They find bugs (including security bugs), they report and fix those, they send the results to major distribution vendors (and it's not the first time Red Hat has acknowledged our developers), as well as mainstream Linux (again, I wrote about it as well before).
And this is how Linux wins: with all the parties contributing to everybody's benefit.