There is no penalty to being told "no". That also applies to "I think I know the answer". There is no penalty for being told "no" there as well, so once you have a reasonable guess why not check it? Disagree with their analysis.
There is an implied penalty because it says about the answer box "Make sure you’re right; you won’t get a second chance" in contrast to "You can test as many sequences as you want" about the sequences.
This is absolutely correct. Perhaps Hacker News culture is such that they realize such a warning can be overcome through a refresh, or possibly an incognito browser window if a cookie is preventing a second guess. Still though, within the rules of the game, there is no drawback of testing negative sequences, but there's a clearly defined drawback of entering an incorrect answer.