It's not a matter of sensitivity -- in this case it's a matter of meanings changing over time, and modern audiences (quite understandably) not quite understanding the meaning of the time. As I understand it, this particular song, the woman's only "pretending" to say no, when really she absolutely wants to spend the night over, and is just making up excuses so that she can pretend later that she did try, guv, honestly, not to get seduced... modern audiences hear the "say, what's in this drink" line, and instantly interpret it in light of modern problems. Date rape *s* an issue and it deserves to be taken seriously, so it's not a matter of being lame.
It's just a clash of meaning. The thing is, such clashes occur all over the place; they did when you were young, even if, perhaps, such things passed you by at the time. Ironic, really, because censorship was if anything even more aggressive back in the day.