This was not the case when I worked in the Federal government. There were different levels and kinds of clearances and while it was true that you could work with less sensitive stuff while the background check process worked its way through, you couldn't go into and view anything elevated w/o the right clearance, or even be in the room pretty much.
This has always been the case, though you generally need to be a US citizen as a practical matter. Whether or not you are exposed to it likely depends on which part of the government and who you are. The common case is when they need the help of outside subject matter experts.
For the sake of timeliness and being able to move quickly, some people in government are authorized to make a judgment about the risk/benefit tradeoff when someone doesn't have an active clearance. It isn't a case of waiting for a background check process, you don't even need to apply. Some organizations will do an informal check of their own in the background if they don't already know who you are. Sure, they would prefer if you already had formal clearance, but it isn't strictly necessary.
I could see many people with this abstract concept of a system that governs itself with it's own rules and policies, not quite understanding that it's all customary.
It's like people thinking that the President can't declassify a document or make foreign policy decisions without the NSC's advice or consent.