He handled it perfectly fine, but only in the eyes of a certain subset of his customers and investors. From this thread it's clear that most customers, and investors are fine with it. I would be fine with it as well if I wasn't paying attention to the thoughts/opinions outside of this club.
What a lot of people outside of this "club" were looking for from Musk is some restoration of solid decision making skills, and that was not one of them.
Sure you can say it's clear from the video that he's not a pot smoker, and I agree with that 100%. But, the problem is most people won't see that. They instead form opinions on GIFs, tweets, memes, and other quick impressions. It's not too surprising that sites that skew older tend to be ones questioning Elon Musk, and sites that skew younger are excited by the guy. I'm not surprised at all that YouTube would be mostly positive as that's where a person would see a lot more of the video which obviously paints an entirely different picture. The demographics of YouTube also skew way younger than the average news site.
If my first exposure to it was from the video itself it's entirely possible I wouldn't have even thought about it as I would have a very similar view as you did. Where I saw him as a non-smoker who went with the flow.
But, that wasn't my first exposure.
My first exposure was on Ars Technica where all the promoted comments are against it.
There is the one that mentions it's still a Federal Crime
There is the one that talks about the context of it. The fact that the funding was secured at 420, and now we see him smoke weed.
The entire thread on Ars Technica saw his action in a negative light, and the vast majority of up votes are for people with comments that are anti-Musk.
Tesla stock falls on executive departures, Musk smoking weed