Actually, it can turn into free marketing against your product. Even if your game is not that terrible, but they want to enforce it no matter what.
The only way marketing against your product works, is if you, as a dev, decide to do nothing to fix the glaring issues your game has. Many AAA publishers have proven this over the years. Lots of Indie devs have proven it as well.
If someone YouTube Let's Play's your game... and they rip it to shreds... Well, that's a learning experience for you. What went wrong? Why? You only need to take the criticism, learn from it, and improve upon it. We live in an age where a finished video game product is rarely ever "finished". It can be altered. It can be fixed. At least, most of the time it can.
All you really need to do is know about the YouTube video, watch it, and then perhaps leave a message saying you're taking the criticisms seriously and you'll be working on a fix for some of the more glaring issues. Maybe even let the YouTuber know when you've made major fixes in case they'd like to do another video on it.
Heck, just getting it out there that you're open to criticism, critique, and making changes when necessary, builds a ton of goodwill with any playerbase. I know as a player myself, that if I see updates for a game that read like, "okay, I'm sorry, I screwed up, the game isn't that great right now, I'm working to fix a lot of the issues", I'm more inclined to come back later and give it another try.
But, in any real case, feedback from people actually playing your game is quite useful. I sometimes do this with my friends. I tell them, "hey, come here, sit down and play this". I then do nothing but watch them. I say nothing. I may make mental notes as they go along, but that's usually it. It's a very useful experience to watch someone play your game who has never touched it before. Watching them think it through and what choices they make in the way they play.
I honestly just imagine this would be a freakin' gold mine to me if someone I didn't know randomly played it on YouTube, recorded it, and I had that to watch.