Hey. Thanks for reaching out. First, I am not a lawyer so don't take any of the following as legal advice. I would warn against this, let me explain the several reasons for that.
1.) Visting Couchtuner the first thing I notice is copywritten artwork displayed within the page. Not only the videos fall under copyright law so any use of the posters, images, etc owned by the studio carry the same penalty as the video itself. Additionally, a studio could theoretically argue trademark infringement by using the names of their productions.
2.) Using external sources for your videos will NOT prevent studios and their agencies from filing DMCA requests against your site. The nature of the DMCA allows reporting organizations to force content offline. There is a process to file a counter-claim in court contesting a DMCA request which can then allow content to be made available again but if you are hit with hundreds or thousands of DMCA reports would you be able to pay filing fees to counter-sue each of them? If the answer is no, then your site would be taken down. I don't personally think it's a fair system but it is US law and we are bound by it and must comply with it.
3.) To the best of my knowledge (and I could be wrong here), there is no case law that would indicate that this type of configuration is any less liable to DMCA claims than hosting the content directly or sharing it over bittorrent. For example, if I share a file with someone by uploading it to dropbox and shooting them the link, am i not still sharing the file? Is dropbox solely responsible? I don't know how a court would rule on this but I would not count on a non-technically minded judge seeing a difference.
Overall, by the letter of the law and our terms of service a site like this could be made to comply but not easily and it would likely not stop DCMA complaints and take-down notices from being filed requiring a response in court to prove your methods are legal. For those reasons I would not recommend running this type of site on any US based host (or at all).