They could trim part of it out. Anyway, there have been lots of songs over three minutes that got plenty of play. I remember a DJ telling me that he’d always play “American Pie” when he wanted a decent bathroom break.
I was kidding of course - that particular “musical gem” never fails to amuse me. But speaking of songs that were off-format time-wise, I can remember going to FM stations when I was a kid to get the long-form version of “Alice’s Restaurant”, which if I remember correctly ran something like 17 minutes. No telling what your DJ friend could do during that if his station allowed him to play it!
The DJ’s at KSHE Radio in St. Louis took a LOT of long breaks. For many years, one might hear something like Court of the Crimson King (King Crimson), Salisbury (Uriah Heep), etc. And that wasn’t even on their “The Seventh Day” show on Sundays, when they’d play seven entire albums in a row, each LP side uninterrupted.
I always figured “Stairway To Heaven” got a lot of play for those bathroom breaks you mention... ;-)