I do not know if that is true or not, but if it is true then his campaign donations are going to be a bit tricky.
[edit] Quick research turned up a bunch of low key contradictions. There are a number of pieces of legislation that assume us-citizen and foreign national are mutually exclusive. Some other bits take dual citizenship into account.
In theory there are a bunch of points where it could be argued that you cannot hold dual citizenship but in practice it doesn't seem to be an issue.
On the other hand it seems fairy clear that some positions, and security clearances require absence of foreign national status (Even then with a little wiggle room, If you've never asked-for or made-use-of foreign national status you can pretend it didn't happen)