Former Google SRE here. Trust me, many of the problems we faced were solved on whiteboards, during chats at lunch, or via email. Most of issues we faced were of a class that simply isn't covered on basic sites like Stack Overflow.
The interview described is pretty much exactly as I remember them. SRE is actually quite difficult to get into, precisely because you need to have fairly deep knowledge on a wide range of topics. The "ways in which you were asked to solve problems" are actually the best way to determine if an application actually knows about what they will need to know.
Heck i'd be worried if your real issues were the stuff solved on stackoverflow :P
not that stackoverflow is bad, but the stuff there is generally a basic/quick reference.
The interview described is pretty much exactly as I remember them. SRE is actually quite difficult to get into, precisely because you need to have fairly deep knowledge on a wide range of topics. The "ways in which you were asked to solve problems" are actually the best way to determine if an application actually knows about what they will need to know.