While taking an aspirin a day is good advice for everybody and no doubt helps to some degree, it has only been shown to decrease mortality in people with atherosclerotic disease leading to heart attacks and strokes. DVTs are different and have different risk factors including stasis (post-op, or extended travel), trauma to the vessel (ie. surgery, torn muscles, broken bones), and any type of hypercoagulable state...makes blood more prone to clot.. (cancer, estrogen use - birth control pills, and obesity).
Thus, while extended episodes of travel alone can cause DVTs, I'm wondering what other risk factors this lady had. Was she taking birth control pills, did she smoke (which increases your risk of thrombosis-blot clots 25 times if a women is taking birth control pills), and was she obese?
The only medically acceptable treatment and prophylaxis for people who are at risk or have DVTs is anticoagulation with either coumadin(warfarin) or heparin (fractionated or unfractionated), both of which have different mechanisms of action than aspirin.

Bottom line there are many things that can contribute to DVTs but you should still get up and walk around every 2-3 hours on those long haul flights! Hope this helps.