Thanks to those who can put their emotions and theorizing aside and be respectable to the OP's request to state facts.
We know that law enforcement has been informing Kaine and Desiree of a great deal of possibilities. We know that Kaine and Desiree have expressed their belief that Terri is concealing information based on things Terri has said directly to them.
We have no idea if what is being contributed to LE are facts. Because we have know way of knowing the context with anything alledgedly said by LE.
We do not know if it was said as a fact or if they lied as an investigative tool. TH's friend claims that LE alledgedly said they have enough probable cause to arrest TH. Is that a fact or did LE lie to scare the friend into agreeing to talk and/or take a polygraph? We do not not know.
We do not know if anything coming from KH or DY alledgely said by LE was a "fact" or a "question" that they assumed as a fact or an investigative tool. An example would be say that LE asked if TH went to ABC coffee shop. Are they asking because a witness placed TH at ABC coffee shop? Are they asking because of a cell phone ping in the area of ABC and ABC has video surveillance? We just do not know why they asked the question. We also would not know if the question is being repeated as a "fact."
Even the MFH allegations. If a landscaper came forward, LE is going to question the fact that he waited over 9 months. LE would have to check his credibility by questioning KH. They might ask him "do you believe that TH would attempt a MFH?" "Did you have any accidents or strange occurrence during that time?" KH might repeat it as a fact when LE was fishing for information to help them determine the credibility of the claims. Again, we do not know if it was a stated fact or a question that was believed to be true by the person being questioned but is really an investigative question.
We also are getting their interpretation of LE's alledged statements/comments. Any broad statements by LE are going to be interpretated by the individual based on their personal feelings/biases towards the person. A statement by LE that they believe TH knows something is not enough information to know what LE is talking about. Knows something about Kyron or knows something about someone else or knows the weather is? The statement is just too broad. But repeated, people cannot help but interject their opinion into what LE is talking about.
Even court documents that state information as coming from LE cannot be believed. Again, we do not know the context. But more than that, just because an attorney states it does not mean it is true even in court documents.
On a personal note, attorneys lie all the time in motions and/or court papers all the time. That is why they use "allegations." But they also lie directly to Judges with very few doing anything about it. The reason is Judge's know people andd attorneys lie. If they did not lie, Judge's would not have a job. If attorneys are sanctioned/fined for lying and/or misrepresentations, in most cases they have to report those sanctions to the State Bar. The State Bar then has to decide if it is something minor or something they need to take action on. Either way, it goes on the attorney's record. Judge's used to be attorneys. They would not want their records dirtied up with a bunch of minor infractions. Therefore, unless it is an extremely eggregarious lie and/or misrepresentation or you find that rare Judge who will not put up with an nonsense, attorneys lie and/or mispresent facts/allegations to make their clients look better. Just because an attorney says it in a court document does not make it true.
Therefore, IMO, anything attritbuted to LE indirectly by anyone else, we do not know the context, so we cannot state it is a fact. Only LE knows if it truly is a fact and they are not speaking.
These are just my opinions and my opinions only.