Near misses happen all the time. I was on OS770 this morning from Pristina to Wien and I almost spilled my coffee over the new tie my wife bought for me last week. Can you imagine the fall out if my coffee had stained said tie ?
On the subject of VLJs the FT ran an article on that very subject this week, apparently sales are rocketing for this type of aircraft, the FT also mentioned that many of these aircraft are piloted by their owners, who I imagine are not professional airline pilots. Though I have no idea of the qualifications required to safely operate such an aircraft.