No, she did not say that she did not want to start right away. She merely inquired about the possibility of delaying her start date. You have an extremely odd, extremist view of language, intent, and desire.
Close to zero employees get exactly the kinds if Hobbs combined with exactly the kinds if working conditions they want.
Similarly, close to zero employers fill a position with someone who mentally, emotionally, and spiritually fill every last desired quality to exactly the right degree.
Employers, employees, jobs, and workers are not machine parts that come in a limited variety and can expect a perfect fit.
You get close and then do a lot if wiggling to make the fit as comfortable as you can.
The fact that the college made the offer meant that they believed that after an extensive search, they believed hat this candidate was the best – not perfect – fit.
In return, W was just testing the wiggle. And it very well might have been the case that even without any more wiggle, this job would have been good enough on the terms offered.
And that’s what the college would have been interested in – “We find you to be the best of the candidates we have. Now, let us know whether we’re the best of the options you have.”
When she tested the wiggle, what they should have wanted to know – given the entire history if their interaction – was “no, we can’t budge on these issues. We want to know whether you still think we’re your best fit” … The implication being that “since we extended you the offer, we’ve already decided you’re our best fit.”
Now what exactly happened here between the two is the question under debate. The stuff about formal letters and etiquette is just rank nonsense. Those are values of centuries past, if they ever were the applicable values in a faculty negotiation. Your worldview about what universities want and what academics are like is absolutely bizarre and alien.