The reason is because when your dataset is in the petabytes, any algorithm bigger than O(N log N) is not going to terminate. You're not going to get any answer at all; your MapReduce is going to sit there burning CPU time for a day, and then you'll kill it, and you won't have any idea what went wrong. (This is learned from experience, if you couldn't tell.)
In a startup context, I'd certainly agree with you - that's exactly the approach I'm taking with my startup, where I'm doing a lot of the debugging and code-wrangling on my local laptop after verifying that the data I want exists and calculating its size with a couple cloud-computing passes. It can sometimes be useful to prototype & iterate with a small subset of the data until you've got the algorithms down.
But many of the algorithms Google cares about don't give any useful results on small data sets. I remember running a few collaborative-filtering algorithms and finding that they gave zero answers because within my small sample of 0.01% of the total data, nobody liked anything else that anybody else did.
[1] Well, it's really the amazing amount of throughput that modern architectures can achieve. Latency hasn't improved quite as much given the inescapable limitation of the speed of light.
Perhaps it has changed as well; when I left (2014) they had just started encouraging engineers to focus on one particular task, with the architecture already defined, while when I started (2009) there were still a number of problems of the form "here's a feature we want to add; here's the data we have available; how can we build it?"
What if you're having a conversation with someone about local politics and you're convinced the local zoning rules don't encourage growth in the way they think they do. Do you force the subject of conversation so you can make sure they know just how wrong they are? Not if you want them to walk away having a good impression of you.
Instead if the talk turns to zoning you put out feelers to see if they'll want to talk about the larger issue, and only engage in the conversation if it seems like the time for it.
The analogy isn't perfect, but if the interviewer wants to talk about the larger issue, you're probably well matched and will have a great interview. If not, and you know enough about runtime complexity to discuss the tradeoffs, then you know enough to just answer the textbook big-O question and move on.
Then there are situations where the code you write must play nicely within a massive, already-complex system, wherein it will work with potentially huge inputs. Like at Google.
So, saying in a Google interview that you don't think Big Oh is super important, and that you prefer shipping whatever correct solution you come up with first and then worrying about efficiency if it ends up being slow, would likely not get you very far.
Let's say you created your own company and you're interviewing engineers.
Would you be comfortable hiring someone who doesn't know the difference between O(n^2) and O(2^n)?
Or someone who doesn't even know what these concepts represent?
There's also the thing I picked up from playing around with graphics demo coding; get the algorithm working first, even if it takes 10 seconds per frame. Then look for the slow parts, concentrating first on the inner loops. Whatever you do, don't try to prematurely optimize the code as you write it, as tempting as it may be. Because almost certainly you'll make things worse than if you waited until after you have a working first pass.
This applies to way more than just fast graphics code, of course.
Any sort of technical solution given at a Google interview would generally have the following questions:
1) What big O time does this algorithm run in? Why? What big O space requirements does it take.
2) If space were more/less expensive, or time more/less important, how would you change the solution and why?
Understanding those tradeoffs and being able to analyze code at that level is a big part of most software engineering jobs.
My opinion is that big-O often ends up being used as a premature optimization effort hindering "just get the right answer first". Maybe that brute force method will work in a reasonable clock-time cost, despite having egregious algorithmic cost. You won't know if you're busy overengineering and optimizing before you even have a working solution.