That's usually not right for incentive options. Check your option agreement. Most will say that the stock option automatically expires or converts to a non-qualified option if not exercised within 90 days of termination without the company having to decide to do anything.
What you are describing is more commonly associated with restricted stock, where the employee "owns" the shares, subject to the company's right to buy them back at par in certain situations.
Lawyers have created all sorts of bullshit to protect the employer and that has become engrained as "best practice"
You're right that you are free to to negotiate a different exercise window prior to accepting your stock grant (and a lot of more progressive companies are offering this). You just can't, under current tax law, get the sometimes beneficial ISO treatment with a longer window.
There's a nice summary of the situation here: https://news.ycombinator.com/item?id=9254299
That being said -- It seems like with some "legal engineering" it can certainly be ameliorated (as was demonstrated by Pinterest). My main point is that if people push for their rights then it will incentivize companies to do the legal engineering that is necessary.
Think about it -- any engineer at these companies can easily leave... but imagine if half the engineers left. The company would go down in flames. People need to work together to have companies pass policies that allow them to have longer periods to exercise.
BTW anyone that understands corporate law needs to understand that the fact that you "must" exercise your options by exorbitant amounts is simply a (very dirty) retention tactic. The company can choose not to buy back your unexercised options at par-value for as long as it wants. The fact that it is "policy" to buy un-exercised options is complete bullshit.