I have taken Ambien off and on for quite some time...I have not heard that or read that in any material...
However, I do think that type of thing can vary from one person to the next though?!? I am coming to the conclusion that oxygen might be a "trigger" for one person and a source of relief for another (ok, for all your serious susan's...that was sarcasm!!! 
)
You might talk to your doctor about a trial basis of coming off that to see if that might be an option? (as far as a trigger?? then again, that might set off a withdrawl/rebound type headache....I swear with migraines you never know what to expect and which situation might be worse???)
Good luck dear...let me know the outcome?
Sara-Migraine/Headache Forum Moderator