If a foreigner is here in the U.S. and qualifies as Resident Alien then he/she files a 1040 just like a US citizen, right. But do they need to include all their worldwide income even if they don't receive the foreign income here in the U.S.

Yes, a U.S. citizen or resident must report worldwide income on the tax return even if received in a foreign country.
If you paid taxes in the foreign country, you will claim credit for taxes paid in the foreign country by filing Form 1116 or can file form 2555 Foreign Earned Income Exclusion.
You may meet another filing requirement is Form TD F 90-22.1. Your U.S. Tax Return: U.S. Citizen or Resident with Foreign Income (http://taxipay.blogspot.com/2008/03/us-citizen-or-resident-with-foreign.html)