It’s interesting to see this question pop back up again, months after the rumor was originally and thoroughly debunked. Let’s set the record straight: No, Issa Rae did not turn down Drake.
Stephen Colbert brought up an old-ass tweet from E! News that suggested Issa Rae 1) once met Drake, 2) was hit on by Drake, 3) let Drake know she was categorically not interested, in that order. Rae, who swears she’s a huge fangirl, was having none of it then, and on her latest appearance on The Late Show, she was equally quick to shut things down.
Rae explains for (hopefully?) the last time: She ran into Drake on her way to HBO’s party after the Golden Globes; Drake was leaving and asked Rae if she wanted to go to the Netflix party. (He also apparently said “I been looking for you all night,” which Rae calls “the most magical words ever.”) But Rae couldn’t ditch the HBO party (the network airs Insecure) even though she wanted to, and she said she’d catch him later.
For what it’s worth, I believe her: that she was caught in the middle between her duty to pay respect to HBO and her duty to hang out with Drake when and if Drake asks you. At least she got this story out of it, which she can tells the next time someone asks her about it too.