Is it possible to update any iOS 6 device to iOS 6.1.6? Apple have just released software updates to fix a rather serious security problem where a valid SSL response wasn't checked properly to ensure it matches the site actually being browsed. I have an iPhone 5, but unfortunately I have a strong personal aversion to the iOS 7 look and feel, so this far I've kept it on iOS 6.1.3.

Other users have better reasons than I to stay on iOS 6. For example, some people might be reliant on an app that has no iOS 7 version (as per bmike's comment), or the device might not have enough memory for the upgrade (as in this duplicate post).

Apple have released iOS 6.1.6 ("Available for: iPhone 3GS, iPod touch (4th generation)"), but my iPhone 5 gives me no option to upgrade to any iOS other than 7.0.6. Similarly, iPhone 4 and iPhone 4S, iPad 2, [new] iPad (3rd gen), iPad Mini and iPod Touch (5th Gen) all ran lower versions of iOS 6 but do not have builds of iOS 6.1.6 to install. 

My iPhone is not currently jailbroken, but I would consider doing so in order to avoid having to use the iOS 7 interface. I'd rather not have to choose between the iOS version I prefer and this security patch for SSL. What options are feasible?
Sadly, no.

The iOS 6.1.6 patch (as was 6.1.5) is an update only available for iPhone 3GS and the fourth generation iPod touch. Apple appears to only be maintaining that branch exclusively for devices which were never compatible with iOS 7.