How should I interpret their silence?
Interpret it anyway you want. They could be slow, they could have forgotten, they could still be interviewing. So If you want to know: ask politely, and accept gracefully whatever answer they give you.
Isn't it rude if they don't send anything?
Yes from your perspective it is rude. But based on experience it isn't unusual.
You expected a response becasue you applied at
"a company known for its hiring procedure (and its explicit rejection
I have seen great variations within a single company regarding how they go through the steps of the hiring process. When I trying to fill a position I have experienced HR support that updated us everyday with new qualified resumes/applications. I have also applied for an internal transfer in that same company that only posted the opening for three days, but then took 3 months to move my application to the next phase.
You may have applied to the slow part of the vaunted company
Now in the weeks since the interview, unless this was not part of a systematic job search, you should have continued to apply and interview. Just continue down that path, there is no reason to wait for company x to respond before you contact other companies. Job searches are not done in neat phases, they involve juggling many opportunities, and many possible paths to a new position.