This hosting service is PCI compliant/certified, which is the level of security we need, and probably this entire conversation is just an exercise in paranoia, but while I'm doing something, I might as well do it as well as possible.
Re^2: Security on shared server
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There's a wipe utility available on most linuxy operating systems (though not always installed by default), but the problem is that journaled file systems don't actually write changes to disk immediately, but rather to a separate journal on disk (which improves reliability in case of crashes). That makes wiping files unreliable, so you might just go ahead and simply delete them.