I find this statement tenuous at best when the example question has absolutely no programming component of any kind and is entirely a little math puzzler about determining the highest floor from which one can safely drop an egg.
It's certainly an interesting problem, and the explanation is presented incredibly well, so I don't fault the site itself. I'm also aware that this is something of a pop culture question for "programming" interviews. However, I don't believe that it is in any sense true that it is necessary to excel at this sort of question in order to be a competent programmer.
This might seem representative of the experience of trying to design a novel algorithm to solve a new problem, but in fact it couldn't be less representative. I've had to write some hairy code in my job a few times, and not once was I under time pressure or expected to have the critical insight within five minutes. Any problem that has any sort of creative or exploratory or "research" aspect to it should not be under time pressure, and ideally it should be mixed in with other work so that you can rest from the problem and come back to it later. The vast majority of candidates who will pass this particular test all the way to the end are ones who just memorized it online.
Also if you couldn't reason your way to the answer how would I have any confidence you could reason any other problem of similar difficulty level. This kind of problem shouldn't you more than 5 or 10 minutes to figure out.
Sorry, we pass on your application :)
In the vast majority of the cases however, you can get away with writing un-optimized code and it generally makes no difference. Considering the egg problem, any computer would not care two shits about running through all 100 floors to drop the egg every single time.
Unless this particular piece of code is a bottleneck for your organisation, there is very little reason to check for/think of an optimal solution to this problem (if you don't know it yet).
That does not make you a bad programmer, just an economical one.