ASCAP policy is opaque.
Radio stations usually take a "blanket" license which allows them to play any ASCAP music without negotiation. (Technically the "blanket license" is illegal, but I gather most stations play one fee for all plays.) While I have heard of play logs I don't think they were widely done in the 1970s (today play-lists are all computer and could be submitted); this may be eye-wool to evade the no-blanket ruling. I had thought that pay-outs to songwriters were based on record sales, not air-play; and their traditional two-tier system meant that top-1000 writers got significantly more pay-out than less-popular writers.
BMI was founded in reaction against ASCAP monopoly and exclusivity. Their policies are less hidden, but they don't bother to explain them well. BMI does say "blanket", which must be a different deal than the mandatory blankets which ASCAP was banned from enforcing.
I don't think the songwriters have any say in who plays their music, or how much of it. A blanket allows all-music DJ shows. Perhaps there is a lesser fee for talk shows which don't use as much music. I suspect the short instrumental-only clips are to suit show format and flavor, not any license restriction.
___________________________
And off-topic: the Happy Birthday copyright suit was settled but the settlement details are not public. This means nobody knows if it is safe to play HB in public. Analysis of the copyright history says it is 99.9% sure expired; but no single infringer wants to put-up the money to fight it all the way to a knock-out. You pay $1.5K to use HB in one movie, the owner collects about $2M/year and expects this to go until 2017 or 2030, so the money is all on their side.