Absolutely. You employer is willing and able to fire you and eliminate your healthcare coverage at the drop of a hat with no remorse, and we should all never forget, and always be prepared for that fact.
The actual contents are almost the opposite, the blog poster stayed around in their role for an entire year while letting their employer know they were unhappy.
I'm all for professionalism when leaving a job. For any full-time position I've held I've always followed the 2 week notice standard as a minimum and have even done part-time work past the 2 week period in a couple of special cases where I understood the burden on the company I was leaving was more than a 2 week transition could handle.
... but I don't see how it counts as being ready to quit at any time if that quitting is the result of the company not being able to fix a job situation you've told them isn't working out for you over the course of an entire year.
Yes, you will need to pay for the coverage that the employer was paying for, but that's not "eliminate your healthcare coverage at the drop of a hat with no remorse".