Can a US pilot fly a foreign registered aircraft in the US?
Yes. 14 CFR 61.3(b) covers this (my emphasis):


  (b) Required pilot certificate for operating a foreign-registered
  aircraft within the United States. No person may serve as a required
  pilot flight crewmember of a civil aircraft of foreign registry within
  the United States, unless—
  
  (1) That person's pilot certificate or document issued under §61.29(e)
  is in that person's physical possession or readily accessible in the
  aircraft when exercising the privileges of that pilot certificate; and
  
  (2) Has been issued in accordance with this part, or has been issued
  or validated by the country in which the aircraft is registered.


So a US license (i.e. one issued under part 61) is allowed as an alternative to a foreign license for operating the foreign aircraft. The other country could have rules on this too, but I have no idea if they would be enforceable (obviously, one country's laws are usually not valid in another one).