Foreign investment isn't fake growth and money being spent in the country is definitely a good thing. It's how Singapore managed to kickstart its economy in the 1960s. Lee Kuan Yew tried very hard, and succeeded, in getting foreign corporations to set up shop in Singapore. The key is to capture value and move up the chain over time rather than getting stuck as a "cheaper back office".

Of course it counts, and should count. Foreign money enters an economy if that economy is producing something the foreigner wants.

A simple bank transfer into the country does not count as domestic Product.

It is local resources extracted, not foreign spent.