1) I guess the first thing that occurs is-- are there other videos on the sites in question that use copyrighted music? ("Be one with the herd" approach)
2) Another idea that sort of titillates me personally is using copyrighted music that's undergone a chord shift. Algorythms will have less of a chance to catch it, for one thing. But for another-- it's just a dang fun alternative!
Michael Jackson's "Beat It," but in MAJOR key:
"Beat it": original in Major key (full) - YouTube
Village People's "YMCA," but in MINOR key:
"YMCA" reworked to Minor key - YouTube
Mucho mas evidencia aqui:
https://www.youtube.com/user/MajorVsMinor/videos
(Bill, have you seen that stuff? Now I'm familiar with pitch-shifting and mashups, but dang)
Covers would be a similar idea.
3) As a long time streetball player (before I got old, hmmph) and as someone who adores Indie music and modern lounge / ambient, I'm partial to the idea of going a slightly different route, i.e. using such music, but actually giving full credit right in the title ("Bball heroics by rising stud [Song: Blibbeldy-Blabbelty by the XYZ band")
Some off-my-head ideas:
Shawn Lee - Cha Love
Shawn Lee's Ping Pong Orchestra: Cha Love - YouTube
Cansei de Ser Sexy - Beautiful Song
Beautiful Song - Cansei de Ser Sexy (CSS) - YouTube
Funky Porcini - This Ain't the Way to Live
Funki Porcini - This Ain't The Way to Live - YouTube
Death By Unga Bunga - Stare At The Sun
Death By Unga Bunga - Stare At The Sun - YouTube
Cosmos Sound Club - Les Chrysanthèmes (sort of a French rapping song)
Cosmos Sound Club - Les Chrysanthèmes - YouTube
My thinking is that such would actually be a way to help out band of choice. Like, when you're a little person gazing skywards so to speak, you're not trying to punish people for repeating your music. You're begging them to do it, in fact!