Dear Wanderlust
As much as it pains me to say this (you know how I love those free miles), I'd encourage you to do the right thing and let Swissair know. You will probably lose the miles but at least you'll have peace of mind (It could save you some grief later on too). And you never know - they may give some miles as a thank you maybe.
It would be interesting to know how the system got you FF number. Maybe someone has stolen your FF number and is illicitly travelling around the world under your name. Well, I suppose it is one way to accrue miles...
By the way Swissair had a promotion last month which was quite good. If you did any flying on Qantas between Australia and Asia or within Australia last month you could be eligible for a 5,000 mile bonus.
cheers Peter