I think this is a dangerous and terrible rule of thumb that will definitely damage culture. It's such an egotistical view that you're so smart, you don't need anyone to help you ever. I would rather work with a bunch of "non-rockstars" than a bunch of assholes. IMO, this deification destroys values like modesty and is generally counterproductive.
If you're really looking to save everyone time, a good balance may be the optimal way. I've seen success with better mantras such as "if you can't find the solution within 10-15 minutes, ask someone". This prevents you from bothering people with Google-able questions, and it saves you from wasting half the day because you were too reluctant to ask the person next to you thanks to your fragile ego.
I feel that when he makes the claim of "never" is where you are having a problem. You really should try to figure things out on your own because that is the only way to are going to permanently attach the solution to the problem. When others help you, the solution doesn't always stick and you are left coming back when you run into something similar months down the line.
Now if you are banging your head into the desk for multiple hours, then maybe you should have asked for help. But as he points out, there are situations where (as a tech lead for a startup) you aren't going to be able to ask for help.
You are taking what he says as "I'm so smart I don't need help" instead of seeing it as "I may not know how to fix this now, but I am determined to figure out a way". You are attaching a very negative view instead of seeing it as resilience in the face of a problem.
The argument that not asking for help results in resilience and therefore debugging prowess sounds like an X/Y problem to me. If the real goal is to have better debugging skills, then more direct advice might be "understand fully why your solution didn't work" instead of "don't ask for help".
Not asking for help / debugging yourself helps you make a leap to a better understanding of the language. You will certainly remember the next time you see that bug and over time, you build up your own knowledge so you have ask for help less. Asking for help is just short-term greedy: solves things now but doesn't help you (or your company) in the long-term.
However, it's good advice if we think about just being competent instead of being a smart deified rockstar.
If you are handed a spec and documentation for all the APIs you will need to use, and instead of reading or thinking about anything you just demand that I walk you through it one step at a time, all day, there is a plain old competence issue and it is wasting time.
Often it really is better for someone to just try to figure it out for a while, even if it takes them a lot longer. You don't learn with people telling you every single little detail.
If you're really looking to save everyone time, a good balance may be the optimal way. I've seen success with better mantras such as "if you can't find the solution within 10-15 minutes, ask someone". This prevents you from bothering people with Google-able questions, and it saves you from wasting half the day because you were too reluctant to ask the person next to you thanks to your fragile ego.