FEC is ONLY concerned with finance and money issues. I don't think there is a federal agency charged with determining eligibility.
When you run for president you file in each state you want to be on the ballot of- there is no Federal election, only 50 state elections (more, up to 60, for some candidates).
I looked for federal forms and could find only state-level forms, mostly for the primaries.
http://elections.delaware.gov/information/elections/presidential_2008.shtml
Here are two Delaware pages. One has the process, the other the form you fill out, and neither has a section for US Constitutional eligibility. There is a mention of “eligible to receive Federal matching funds under the IRS code” but I bet the IRS does not check to see if you are a “natural citizen”.
Bottom line, I think there is no real process to check- no “controlling legal authority”!
I can't do more research now, maybe someone else can look up the IRS eligibility issue?
What about the fraud element? Surely its illegal to pass off a forgery as the real thing, especially in these circumstances.