So, what's your feeling on the matter?
For me, it's simple. There is a bigger and better goal than knowledge. Understanding!! Of course, having knowledge or where to obtain knowledge is part of understanding, but memorizing or looking stuff up is only a skill. Understanding allows you to apply the information to the current situation and to, possibly, other situations. Going even further, abstract thought is not Google-able (well, the definition of abstract thought is, but that's not my point). It may be that abstract thought is the key to being the special beings we are, so I give it a lot of credence.
One other point to consider is that there are other search engines besides Google. Search engines are not the receptacle of information, but mainly quick researchers who can find possible sources for our query. To me, that means the internet is actually knowledge/information, Google is one of our research assistants, and it is our job to use the information gathered quickly.
There are good reasons to have some (or as much) of the information in our brains and to not rely on the internet. One is the constant battle against advertisements or biased search results (pay for your ranking) due to revenue streams. Another is not requiring the internet to be able to do everything (a crutch). But one aspect not mentioned in other articles that I have read on the subject stands out: if you don't have the information in your head, your subconscious cannot work with it.
We often forget how important and tireless our subconscious is. For example, you know how it is when you cannot remember something but it's on the tip of your tongue. A few minutes later while deep in the middle of a completely new topic of discussion the answer pops out. That, my friends, is your subconscious at work. I am no expert, but surely there is a connection between dreams (awake or sleeping) and the subconscious. If so, isn't information assembled as knowledge in our own little brains the ingredients to dreaming, abstract thought, creativity, etc? And you can bet that most of the ideas that you have don't pop up instantaneously. Instead, your subconscious has been motoring along for a while on the idea and if finally got formulated in a fashion that the brain considered to be worthy of the front page (the here and now).
So, I am all for Google being the place that I can look up trivia and song lyrics and how tall Nathan Fillion is. But, I want some set of working information in the brains of all my students so that they can get to it quicker, make it work for them in the future, and maybe become part of their dreams.