This point about banning countries he doesn’t have business dealings in is probably a bit coincidental, since his Executive order used an Obama-era list to determine the countries to ban. This list merely compiled countries with significant terrorist activity, and was forced past Obama’s desk on an omnibus spending bill by congress.
http://www.snopes.com/trump-immigration-order-obama/
The thing with Executive Orders is that they must reference specific legislation, since it is not (supposedly) in the Executive’s power to legislate. Now I would bet that if Trump didn’t have business in Saudi Arabia or the UAE, he would have found some legislation which included those countries. As it is, we can only speculate as to the why of all this.