Also, regardless of whether or not it is racist (it is, just so no one jumps on me!), the term is etymologically/geographically/ethnically etc incorrect.
For the other "Stans", the descriptor for the people is Afghan, Uzbek, Turkmen etc - not Afghani (which is in fact the currency). So even if Pakistan were like Afghanistan, the shortened form would be "Pak".
However, the country Pakistan is based on an acronym from the 20s or 30s referring to the names of the relevant bits of the north-western provinces of the British Raj (not all of them feature, but Punjab, Afgania (the North West Frontier) and Kashmir are the P, A and K of Pakistan). So there has never been a Pak people, so neither Paki or Pak are correct.
Ignoring all that, which is irrelevant, whilst being of interest to me, the term in this country has been and continues to be used in a pejorative fashion. As such, given she isn't Pakistani, she can't "reclaim" the word. And to compound the offence, she is talking about someone who is Indian - she really isn't coming over well at all. At best, she doesn't care that she is using offensive/racist language. I personally would read that as she is herself racist.