Transparency is necessary for security. Full transparency requires free/libre software---we need both transparency for the implementation, and transparency for integration into the system as a whole (and, as it follows, the whole system).
Even if the system purports to be secure, that doesn't necessarily mean that it hasn't been tampered with, or that a backdoor hasn't been installed---we've had a number of examples of this lately. A fully free, reproducible system is needed here.
There's an often-used argument to dismiss this concept: that free software can still have security bugs. And then they cite recent issues like "Shellshock" and "Heartbleed". Freedom doesn't guarantee security, but it has stronger assurances than proprietary systems, where you don't even have the chance to look at and study it (to any reasonable degree); and you (collectively) definitely aren't able to modify it to suit your specific needs, study its integration with the larger system, or build it reproducibly.
Any other arguments that can be applied against free software can be applied more strongly to non-free software.
Corollary: Confidence in the security of a proprietary, secret system is always less than a free/libre, transparent one, even if the free system is provably less secure overall.
In a fully free system, it is not possible to lock down users, as the OP was concerned, because someone will just modify the software to remove that anti-feature.