Commercial Audiovisual Media Copyright

A member of our ward wanted to show a commercial movie at a ward activity and was told by a member of our Ward Council that, "It's approved as long as we have a paid streaming service. And that while we needed approval from salt lake, streaming services release liability through a paid subscription." But I can't find that anywhere in the Church Handbook or church announcements. She is hoping to stream something from Netflix, Amazon Prime, or Disney+.

If this is allowed, is there documentation somewhere that states this?

I'll refer you to General Handbook 38.8.10

Can I show commercial audiovisual products at Church functions?
Generally not. Church members should not violate warnings and restrictions that are placed on commercial audiovisual products. This includes movies, other video, and music. Using commercial audiovisual products at Church functions generally requires permission from the copyright owners.

What permission is needed to present musical and theatrical productions?
Productions that are owned by the Church or IRI may be performed in Church settings without permission from Church headquarters. If a copyrighted production is not owned by the Church, members must obtain the copyright owner’s permission to perform all or part of it in a Church setting. Usually the copyright owner requires fees or royalties even if no charge is made for the performances. All presentations should have the approval of local priesthood leaders.

If you look though the terms of use for the streaming services, you'll probably find that it's restricted to "Home use". Showing it at church is NOT "home use", even if there is no admission fee. There might be a subscription service that does allow for non-home use, but I'm sure you'd notice the price difference.

If you get written permission from the copyright holder, then you're fine. Some commercial movie-makers that aim at a church audience may willing to grant permission at no cost. Our ward did that many, many years ago. The movie might have been The Singles Ward, but I could be wrong.

The member of your ward council is wrong. The emphasis in all of these is mine.

The Netflix service and any content accessed through our service are for your personal and non-commercial use only and may not be shared with individuals beyond your household.
Netflix Terms of Use

You agree that as a condition of your license, you may not and agree not to ... use the Disney+ Service or ESPN+ Service for any commercial or business related use or in any commercial establishment or area open to the public (e.g., lobby, bar, restaurant, diner, stadium, casino, club, cafe, theater, etc.) ... whether or not for profit.
Disney+ and ESPN+ Subscriber Agreement

Subject to payment of any charges to rent, purchase, or access Digital Content, and your compliance with all terms of this Agreement, Amazon grants you a non-exclusive, non-transferable, non-sublicensable, limited license, during the applicable Viewing Period, to access and view the Digital Content in accordance with the Usage Rules, for personal, non-commercial, private use.
Amazon Prime Video Terms of Use

When we have done the in past in wards I have been in, we either worked directly with the production company to get approval or purchased a license through Christian Video Licensing International.