No, it is not that at all. It's like a Judge Judy episode when she says, "If it doesn't make sense then it's a lie." Now, yes, different people may react differently, but in actuality, on average, people don't. The reaction to the offense strikes many (and I am one of them) as wildly disproportionate. Spock has never struck anyone as being that emotionally unstable or fragile especially over the long haul. It is an emotionally non sequitur reaction when factoring in how self-aware Spock is. And the notion Spock would refuse her earlier overtures to make amends just doesn't add up.
Now to be clear, I am not poo-pooing the storyline as merely pointing out a weakness within it (Like Kirk not raising the shields in The Wrath of Khan - still love the movie and all involved and know it was to service the plot but hey that bit was terrible writing). Star Trek Discovery has moments of great writing and moments of not so great writing. The Spock-Burnham exchange and fallout does not ring logical or true.