Statements affirming public data are fine.
Stars and watchers on GitHub are public data - anyone can see it. If you're just making a statement about that data, you're fine - you're stating a fact, what people choose to make of it is out of your control. Something like
BigCompanyA and BigCompanyB have starred this project on GitHub!
would be okay, for example.
I'd steer clear of making statements based on the implications of that data. You know (for a fact) that the company has starred/watched your repository; however, that doesn't necessarily imply that they use the project. They might just really like you. Unless you know for certain that they use it, I'd avoid saying they do.
If in doubt, ask!
It sounds like you already have a channel of communication open with the people you're planning to claim as users. If you're not sure whether it's okay or not, use that communication channel to ask them! A quick
Hey, do you mind if I quote you on that?
Hey, can I list you as a user of this project on my website?
isn't problematic - you can even tack it on to the end of a more business-focused message, if you like.