The lady (servant - according to the article) was brought in on an authorized "Au pair" visa. Indian Diplomats in the US are paid little in-terms of monetary benefits. Most compensation is in the form of "perks" that help in their day-to-day lives - this "au pair" benefit is one such perk.
While in the US this "au pair" ran away despite being (apparently [2]) treated well. Then there are serious allegations that she contacted a lawyer thru whom she tried to extort the diplomat [3].
No one is implying that having a "servant" is a right. Having an "au pair" was an accepted & Authorized perk. The article starts off with a wrong-headed premise and does some hand-waving from there.
Also see https://news.ycombinator.com/item?id=6947473 for the real motivation behind this incident.
[1] http://www.firstpost.com/india/adarsh-scam-devyani-khobragad...
[2] http://www.dailymail.co.uk/news/article-2526719/Pictured-The...
[3] http://www.americanbazaaronline.com/2013/12/18/richards-dema...