What she is being told is complete baloney. See this question here for example, and this Motley Fool article republished on the Nasdaq site.
In order to trade U.S. stocks, the easiest thing to do is to open a brokerage account with a U.S. broker. However, brokerage firms have different procedures for non-citizens based on their residency status, and non-citizens therefore have to produce more documentation in order to comply with their internal rules.
There is no residency requirement, once the account is set up. If she already has a brokerage, then that part is done.
I can't find anything definitive on the SEC website, but this page gives advice to foreign investors against getting scammed:
We encourage all investors to thoroughly investigate any investment opportunity and the person promoting it before you part with your money—especially if you are a non-U.S. investor seeking to invest in U.S. stocks.
Your friend may want to push back against the broker. It may be that they just don't want to fill out (or don't know how to fill out) the paperwork required.
Based on Tim Day's comment, I'm wondering if it's an issue with shares and having somewhere to deposit the proceeds. They may require a US bank account for that. But even there, the residency requirement is BS. I opened a bank account on the day after I landed in the US. I just had to have appropriate identification.