Unless there's a company initaitive to use crunchyroll to empower playstation or vice versa. This is pretty normal. Sony makes chips for their compeitors. Samsung makes chips for the their compeitors. Sony buys Azure from Microsoft. Netflix uses their competors cloud services to run their streaming services. Apple used to use Bing for iPhone search and Azure for cloud. Warner Bros makes shows (even DC shows) for Netflix even though they have multiple streaming services.
Unless there's someone higher up stopping it for a wider strategy it's not uncommon for companies to work with compeitors espcially if compeitors have multiple busineses.