Something like this used to be the case in the US and to some extent still is, but I'd say it's more like a spectrum and one with lots of variation. Comp Lit departments are changing too (when they're not just disappearing). In many cases, they're increasingly home to scholars of non-Western literatures that may not have a place on campus otherwise. English departments are also becoming more theoretical and interdisciplinary in many cases and less tied to the traditional canon (though there are still old-school programs). One way to get a feel for this is course requirements. A stricter set of distribution requirements will often indicate a more traditional program.
As a matter of good scholarly practice, it's usually frowned to engage with your primary material only in translation, which holds true throughout the humanities (though you may still provide translations in your scholarship depending on your audience. An exception may be made for theory but even then its better to have a basic reading knowledge of the original to understand terminological issues). Most English departments, however, do have a foreign language requirement and would welcome your ability to work in multiple languages. However, if the majority of your primary texts are non-Anglophone, you might not fit will in an English department. But if you want to work primarily with Anglophone media and occasionally incorporate non-Anglophone texts by way of comparison, that could certainly be done in the right English department. None of this is to say you should go to an English department, but I wouldn't rule out that possibility to quickly. And it's also good to be aware of the potential pitfalls related to comparative literature programs.
Two questions that should help you get better responses:
1) What's your end goal? Would like to obtain an academic position in the US or would you rather go back to your home country following your PhD? If it's the former you should know that there are very few jobs in Comparative Literature departments. This isn't to say you should't enter such a program, but you should be aware that if you do, your best chances for a job are apt to be in national literature departments. Which leads to my next question....
2) What languages do you work in and what in what languages are the works of literature/film/media you would like to research? If you're primarily interested in anglophone literature/media, it may make sense to look at English departments. Many (though not all) English departments have strengths in and advocate interdisciplinary methods and engaging with theoretical perspectives like ecocriticism. Same goes for German, French, etc. departments. So just because you do interdisciplinary/theoretical work, doesn't mean you couldn't have a place in a more traditional department.
LineOfFlight got a reaction from Rrandle101 in Comparative Literature 2020