Grrr... made a video from my vacation, but can't upload it due to the song I picked

[LeeH]

Went to Belize last week and took a fair amount of video. I edited my video down and grabbed a song off of my wife's iTunes library (ie one she has paid for). When I upload the video to Youtube or Facebook I'm immediately told the video has been removed for copyright violation.

Youtube I get. Anybody could watch the video and would therefor not need to buy the song. Facebook I don't get. The video would be viewed by 25 people max and this would likely be their first and only exposure to this song. Wouldn't this fall under fair use?