Does it really take more than 3 weeks to get a book or is PBS just padding their estimates so that people will be happy when it doesn't take that long?

It all depends. Media Mail can take 3 weeks or longer. On the other hand, Media Mail can also move as fast as first class mail. It seems most books average about a week to two to get to me, but I've had some take longer--including one that was one state over that took longer than a book from the West Coast.

It seems to me that books I mail to certain states get there fairly quickly and then there are other states where I know it will take longer. I'm in PA and I find books I mail to Arizona always get there fairly quickly while books I've mailed to some states in the Midwest take longer.

Remember also that not every book will be mailed Media Mail. If you order a paperback that's less than 6 ounces or so, most likely it will be mailed first class and should take about the time a letter would take.

I just got my first book today, postmarked Sept 29, so that one only took 2 days.  I would have to say that if one took a few weeks I wouldn't freak out seeing as how it's basically free, but it was really nice to have the first one come so very quickly.

It's actually better than it was when I first joined nearly 3 yrs ago. It was the norm for books to arrive within a day or two of the 4 week time estimate. I got used to never planning on when a book would arrive, and have never even worried about them until the are about a week over due in the past couple years now. Even tho the PO is better, it's still not uncommon to have a book show up a few days after it's been declared lost. Why do you think they have that button?