I had an issue with this as well. The author implies that startups "often" fire employees before they reach their 1 year cliff to avoid paying out equity. That's silly on so many levels.
The most infamous case of this was Zynga pre-IPO where certain employees were pulled into a room and given the "give up your unvested equity and keep your job, or lose both".
I'm not sure if it's common, but it's definitely not unheard of.
Anecdotally from conversations I've had with founders some are very, very keen on cycling options back into the pool as much as possible. More importantly I've heard some ideas on how to do this that made my skin crawl.
The most egregious and common one I hear is back-loading options vesting (e.g., vest 5% in 1st year, 10% next year, etc) - note that Amazon already does this, though standard is still linear. Dragging out the frequency of vesting is also common to try and create as many unvested options as possible when an employee chooses to leave the company.
One big takeaway I've had from these conversations is how many founders do not see equity as compensation earned, but as some sort of gift to be granted to the virtuous and loyal.
It's a little depressing that the frank answer to "why not vest quarterly" has been "because if they leave we don't get as many options back". It's interesting that we never think about cash compensation that way but do for equity compensation.