I guess part of the problem raised by the OP might be how we determine (assuming we have the same definition of what a fact is) whether a piece of information fits the definition. If I consider something to be a fact, I should be able to explain why I think that's the case. It could be through direct knowledge or experience, it could be because someone I trust told me it is so. There is nothing in this rationale that necessarily means you must accept my rationale. You may not have the same experience as me on the same matter, you may not trust my word or judgement. So something can be a fact for me, but not a fact for you, perhaps because you don't have enough information to establish it.
Sometimes exactly the same piece of information may be a fact for one person and represent a different fact for another. For example, I think my favourite t-shirt is maroon, my partner insists it is brown. I am certain I am correct, but am I? Of course sometimes whether a thing is a fact is subject to our judgement.
it could be that a person does not accept our facts for a number of reasons I can think of:
1 We're wrong and they know more;
2 They don't accept our assessment;
3 They don't trust our judgement;
4 They don't have all the information we do;
5 They don't trust some of the information we consider reliable and have used to establish a fact;
6 They believe they have already established the fact and are not prepared to consider an alternative view.
There are probably loads more reasons why a person would reject something we are convinced is a cast-iron fact.