My few pennies worth would say it's not too hard to do 250 hours in 16 weeks, although I've never heard of it being done that quick. I'm guessing this timeframe if quoted, is just for the flying. Of course you need to do theory exams, medicals etc at some point. It sounds like an awful lot of hours in 4 months (16 weeks), but it's only 2 hrs 15 mins a day!
I did a PPL (45 hours) in 3 weeks a good few years back- which works out the same rate per day +/- a few minutes.