The article is 4 years old. I'm not saying it was a smart move, but at the time he would have had to pay taxes that he might not have been able to afford. I know people that left SpaceX options on the table because they couldn't afford the taxes.
EDIT: See https://www.esofund.com/ There are other newer places also like https://join.equitybee.com/
Also, brokers who create a secondary market for this equity will also arrange financing, but it depends on the "hotness" of the equity.
SIDE NOTE: If you have SpaceX stock, and you're going to leave it on the table due to taxes, reach out to me and I can arrange for something also. But go to ESOFund, etc first of course - those are professional outfits.
18k isn't a small chunk of change, but it should be managable by most engineers. going from 4000 (.27*15k) to 20+K is a big jump, but it shoudn't be what scares you away.