Yes, I think that they need to stay a lot in the country that they came from and that that is the country that they need to try and help out the most, not the ones that they are just going to later on to try and make a ot of cash.
I believe that companies should have and maintain a strong presence in their home country. Companies should have a responsibility to help boost the economy in whichever country they are based in. It helps to keep jobs in that country which circulates the money back into the economy. Pushing jobs and money out to other countries may save then money, but it only hurts the home country.
International companies have a responsibility to maintain a strong presence in their home countries. Their country has allowed them to set up shop and run their business assuming they abide by local, state, and national laws for business. For setting up and operating in a country they should feel responsible for having a strong presence to their citizens.
International companies do not need to create artificially large presences in their home countries. They have some responsibilities, such as paying taxes and supporting their home countries' institutions, but if their core businesses are located in other nations, they should be allowed to pursue these avenues without worrying about the presence they may or may not have at home.
Large businesses must do what is best for their shareholders and stakeholders and if their home country is not a large market for them then I see no reason why they should have a responsibility to have a strong presence there, I do feel that it is likely good for public relations reasons to do so though.