I know that one way they do this is through using what they call a leap smear instead of a leap second. Yesterday, instead of having 11:59:59 twice, they evenly distributed out the second over the course of the day.
The fact that basically no computer system in the world allows for a 61-second minute is just a failing in almost all time libraries to adhere to the standard.
(This is a fancy way of saying "Time is a quagmire and writing code to properly handle time is an exercise in optimizing ulcer generation" ;) )
I believe GP is incorrect (or rather, the overall point that most NTP servers followed the standard and Google's didn't is correct) and most NTP servers did have 11:59:60 as per the standard.
And oddly sad. ;)
Even if you waved a magic wand and made all computer systems in the world compatible with 61-second minutes, it'd still cause problems because people aren't going to know what to do with it. Imagine what happens when a non-technically-savvy person comes across a time that looks like 23:59:60.5 on something at their work. They'll immediately think that's some kind of error.