If you’re a small brand, you can be the first to own something big, but aside from the credibility issue, the other danger is that a bigger brand may come along and steal it.
That said, there are exceptions.
1.) By owning something big, this may create a perception that you’re bigger than you are.
2.) You may be able to own something big if you put a different spin on it.
3.) If the subject you wish to own takes a social, political or moral high ground, often a smaller, braver brand is more appropriate.