Who and what are Luddites?
What are the nature of these foreign investments? Do they invest in stocks, bonds or government debt? Isn't this going to effect the value of the dollar eventually?
Luddenites were 19th century folks who were so concerned about machinery putting people out of work because of its vastly increased productivity that they destroyed the machinery.
Foreign investment can take the forms you mentioned as well as buying companies outright. Investments increase the value of the dollar because they must buy dollars to make them. Japanese auto companies use this method called "direct foreign investment" as well as buy a lot of government bonds.