Can couples get sealed in a temple despite being married to someone else? For example, could Lori and Chad have been sealed to each other before Tammy and Charles had even died?
Short Answer: No.
Long answer:
To be a living couple (because work for the dead is done there too) wanting to be sealed you have to have these things:
1. Both have to have valid temple recommends meaning they had worthiness interviews each with their bishop and again stake president (or counselors)
2. A LEGAL marriage license either from a civil marriage in the past, or one that permits a legal wedding to take place between the two of them that very day. (Tough to do if you are still married to other people legally)
3. A sealer to perform the ceremony. This is a man who has authority in the church through his calling to perform the sealing ordinance (ceremony).
If you have been married before and are divorced, then you need to have a sealing cancellation done (if you're a woman) or a sealing clearance done (if you are a man). Deceased spouses do not require any additional work for men, but they still require cancellation for a woman.
The account I have heard does not indicate that they had a sealer perform the ceremony because they would have to show him a legal marriage license which we know they would not have had while married to other people. It's been known to happen, but it's usually tough to pull off. And it does not sound to me like any sealer or anyone with proper authority in the church performed any such ordinance. Not to mention - there would be a record of it though records for living people are not visible to any but the individual and the lay clergy their membership records are held by.
Based on this couple's track record, I would say they no longer believe that laws, either of men or God apply to them. They don't seem to think the church's actual authority matters much if they believe they are "above" such matters which their behavior indicates. Thus, I believe that they had their "friend" "seal " them in a pseudo ceremony that THEY feel is valid. A lot of what they are doing and the way they are going about things are very much outside the bounds of the order and structure of the LDS church.