For most users I could not agree less.
To me, the essence of that quote is that any sane security model must include the vendor as a threat, but when I do not have control over my own hardware and software, I have little to no ability to respond to that threat. Moreover, without access to source code, I have little to no ability to audit my own security. Fundamentally, I do not believe in the idea that security can reasonably exist without auditability.
Or anyone who gets access to the vendor's database.
If the vendor is in control, you aren't secure.
Open-source and closed-source software really isn't all that much different for users. All the differences require you to become a professional in the field, or a subset of the field before they mean anything.
Can you say "I would like to keep using Exchange, but I do not trust Microsoft, so I will switch to another vendor"?
PS: this has to do both with open source and open formats as well.
Security is one concern of many. The overriding one being business value. Using Exchange as an example, it would be difficult for me to come up with something that matches its value. I don't, however, trust it. As an aside, I trust Gmail even less, because at least Exchange runs in an environment I control.
And therein lies the solution. Defence in depth. It's a process, and should not rely on any single product. Open- or closed-source.
I might choose to protect myself against external, internal and vendor attacks (unintentional as well as malicious) by installing a network firewall, a proxy service, and an application firewall. I might then deploy access controls that authenticate users and authorise their access based on certain criteria. I'd devise a patch strategy. I'd implement an audit policy. I'd do a whole heap of stuff.
Frankly, the argument for either open- or closed source is getting tired. Any threat can be mitigated. It's success depends entirely on the value of the asset being protected, and the amount of money you're prepared to spend protecting that asset.
Apologies, I wasn't very clear.
That said, compromising a sysadmin account in Exchange does not yield email content. Assuming service accounts have been correctly configured (ref. security policy). However, a Gmail sysadmin can have (and has, in the past) access to users' email content.
If I wanted acess to anyone's email account I'd opt for a social engineering attack on that user directly. Given history that's the easiest vector.
If you think advocating defense in depth as a strategy betrays a lack of understanding of security then, well, damn.
Actually, the user doesn't have to trust anyone: the user can ask more than one party to audit the code. In fact, with open source, there are, usually, many different parties already auditing the code.