Basically what happens is the trafickers put adds all over eastern Europe advertising jobs in western Europe. The girls apply for the jobs thinking they will be waitresses or something like that. Then once they are out of their country they find out the truth, but they can't do anything.
I think you have a point and I understand why you balk at the word "kidnap".
From the stories I have heard, what usually happens lies in a gray area between a kidnapping, a con game, a seduction... Just as example, some slimy guy has an office downtown that nevertheless looks like a semi-legitimate business promising/advertising "work" in some foreign country. Young girls from poor families who need the money desperately show up to "apply" for the "job". (Which is, supposedly, being a maid in some rich household, or something.) Everything seems on the up-and-up (at least to a naive 17 year old girl from the country) but the guy says "of course, we'll need your passport..." Transportation is arranged for the girl to go somewhere (whatever foreign country), but upon arrival her passport is strangely withheld, or just taken, from her.
Now she can't leave, has no money, and has no options but to go to work as a prostitute for whoever has her. (This all is more the type of story I hear coming out of Russia, but I suspect something similar goes on in these cases...)
Now, maybe this all isn't exactly the type of "kidnapping" we're familiar with (which calls to mind a girl disappearing without warning, guys jumping her and grabbing her and pushing her into some van, blindfolded, etc.) but the effect is the same. I understand your suspicion at the large numbers but I think it's because you're misinterpreting what people mean by saying these girls are kidnapped. Substitute "tricked" or "coerced" if you like. In a court of law it would all probably still be considered kidnapping. And so in the main I don't really doubt this story.
It's quite real Skywalk.