OMG BEST THING EVER, HOLY SHIT, IM SO JEALOUS! WHY DID I DON’T HEARD ABOUT THAT BEFORE!!!!
‘There’s no way that’s true’, I thought, but someone on this post said it was on the commentary, so I went and listened to the commentary. No mention at all of the kiss being unscripted, but a mention of what notes the director gave to Billie and David: “playful, both obviously enjoying it”.
Plus, in the Doctor Who Companion Series Two (page 25!) it notes that the script said “after kissing the Doctor, Rose/Cassandra ‘wipes her mouth like she’s eaten fried chicken’”. So no – it wasn’t unscripted.