I earn a living from my SaaS. I am a solo founder, responsible for everything. I wrote all the code. My customers pay subscription fees because the software makes their work easier (it's a B2B SaaS,
https://partsbox.com/).
Bugs are solely my responsibility: there is no one else to blame. And bugs mean that my customers paid money for a product which did not work as intended (certainly not as I intended it to work). I feel it is definitely right to apologize for bugs!
I disagree with the author: if I worked at a workshop and dropped a hammer onto my customer's foot, I should apologize. No matter what the reason: I could be clumsy, or you could say that no one could be expected to never drop a tool — still, an apology is in order, because I did drop that hammer, and it made my customer's day worse.
Therefore, I always apologize for bugs.
What I did, however, learn to do, and it is quite important, is not to apologize when you are not sorry. An example is when a customer is unhappy with the pricing, or complains about a missing feature. Many people will begin a reply with "I'm sorry, but…", and it's the wrong thing to do. I only say I'm sorry when I really am.