At no point did I get "rush hour" from the dictionary hints.
Just one of those phrases that you have to learn by getting it wrong, apparently...
Possible definitions provided by peeking: tip, end, and something other than peak.
In English we would tend to say during the rush hour, or in the rush hour, not at the rush hour, since it is a an event that takes time, not a destination.
Might be a regional difference, but "at rush hour" feels fine to me. Rather than a "destination" though, I'd say you're referring to rush hour as a particular point in time during the day, similar to how you'd say "at 6 o'clock".
i intuitively thought the same, although the sentence didn't say something like durante or mientras...
Google Translate says "At rush hour" which would be more correct in English.