It's not really a case of lying to the BATFE.
All they require is that you meet the criteria to fall into on of the "exceptions" with regard to the phohibition on the importation/possession of firearms by non immigrant aliens.
I once spoke to one of the BATFE's "Examiners of Legal Documents"... or something like that... She told me that as long as an app meets the "letter of the law" it will be approved.
I use a Hunting Lic. from the state of Alasksa... 'Never been to Alaska.
Now like I said before... Having a flyer/invite/screen capture giving a few details about an event you're attending in your hand when you actually cross the border can help, but it's just to support your "stated reason" for your visit...
'Same could be said of driving to Chicago for a wedding.
'Buddy did that last year and when the BPO asked why he was going to Chicago and he said.."To attend a wedding" the BPO asked... "Do you have an invitation I can see?"