By 1st run, he probably means 1st run over a tv network. BB@H has Epix and you can stream Starz content from VOD. So there is some 1st run stuff available.
There is some as prinestar31 points out. But those channels in general are not HBO/Showtime - like where they get first TV run movies. Of Course grouped they cost less also.
Epix has three channels on BB@Home and many are newer movies. The other 12 movie channels have lots of old movies and lots of movies that were released after the year 2000. I remember when I first got HBO on my 12 foot dish, I watched every movie that they showed each month. From what I remember there were around 30-40 different movies. Wow, what a change. Back in those days HBO was not scrambled on the big dish, so it was free, but their was only HBO East and HBO West.