It is my understanding that the use of sweetened condensed milk is not an aberration, but actually one of the distinguishing features of authentic key lime pie! That screenwriter was wrong.
I have read this many places, but here is the history in a nutshell from a Florida Keys website:
Because of the Florida Keys isolation before the railroad was opened in 1912, fresh milk was hard to come by. So Gail Borden?s invention of sweetened condensed (canned) milk in 1859 came in handy. It also meant that you could make a custard pie without the necessity of cooking it. The Key lime juice by itself was enough to curdle the condensed milk and egg yolks. No one knows who made the first one. They were probably made with pie crusts at first, but soon the Graham cracker crust became the standard.
Now, don’t get me wrong. I think that a custard pie made with a cornstarch-thickened filling (i.e. like FRESHKID linked to) would taste fabulous with key limes. And my mother makes a pretty killer (if a bit puckery!) lemon-lime meringue pie, so I know lime juice is great in that type of pie, too (most lemon pie fillings use egg yolks, cornstarch, butter and sugar, but not milk). I bet you could even make a creamy key lime pudding pie. But the “traditional” key lime pie really does use canned milk.
I think it is important to use key limes and not persian limes if you can help it. You might need to add more sugar if you use Persian limes, but the tropical key lime has a distinctive flavor that to me, is really the star of key lime pie. I wrote about key lime pie here and there is my own so-basic-I-can-barely-call-it-a-recipe recipe for Key Lime Pie. My brother requests it every year for his birthday.
I have made it with all kinds of scratch pie crusts, but like a graham cracker crust (or one with a not-too-sweet cookie) the best.