Well - first of all, I don't think they do get so many people in from developed countries anymore.
The ones they do get in from those countries, are people who are 'ripe for the picking'; they usually are emotionally vulnerable and have a need to escape into something, something that will help them cope with life. When someone then comes to their door (no effort from themselves except perhaps prayer), they bite. They may be happy that someone - anyone - would come to their home and talk with them about issues they've been troubled with.
So... The internet then?
Remember that we've all been Witnesses, and we weren't necessarily stupid. I remember when people would say "Why do you live your life by a book and listen to what a bunch of old men in Brooklyn tells you? Why don't you think for yourself?" I felt insulted but also a little 'bewildered', 'cause I felt that I absolutely did think for myself. And I did -- based on what I had learned as a JW. I can not say I remember feeling that I couldn't research things - that I couldn't go to the library and borrow any books I wanted for instance. However - I did of course not borrow books that were critical to the Bible or to JWs, because I had been told that those were just lies anyway. Also - let's not forget the belief that Satan is pulling his strings... My personal excuse is that I was born in, and was never taught critical thinking and logical reasoning.
When they come to people's door and start really talking to them (the people who will listen), there are several methods they can use to make them stop scrutinizing the religion. We all know this if we think about it, 'cause we've all used them. "If you have questions, you should ask us - if you had questions about the liberals, would you then ask the conservatives, or people who had left the liberals to become conservatives?" ----- "The negative things you read on the internet are fabricated by apostates - they do all they can to taint us." That's why it's so important that we "apostates" are honest in our research, and are able to document what we say. If they can point to only one small error in what "apostates" say about JWs, or something that is blown way out of proportion, or someone behaving irrationally, that would be enough for them.
That said, "apostates" can't really ever be "good enough"; we can always be used as an example of what happens when you leave JWs, no matter how 'good' and accurate we are, simply because we are not JWs anymore. For instance, a JW could say to the 'door': "JWs are a morally clean people. You'll notice that when people leave and become apostates, they start smoking again, having sex out of marriage, become homosexual, start celebrating pagan rituals, lying... any of those things." If the 'door' is already a religious person, it won't be long until the JW has him/her wrapped around their finger, reading cherry picked Bible verses.
The various end time dates etc. available for research on the web are again explained away with 'apostate lies'. Old literature is hard to come by even for devout JWs. 'New light' not only accounts for new understanding, but is proof that God is still behind them... Again - all this will only work on a few people nowadays, at least in developed countries. But I'm sure there are still some out there who are vulnerable and need something to believe in. The JW beliefs can be refuted using the right 'tools', but they have a rather 'well polished' belief system that they can use to answer most questions.
That and... there's a sucker born every minute.