"mere fact" can also be understood as a reference to a very small fact. Thus, a single and very small and apparently unimportant fact can be used for some comparison. For example, one might cite this fact as a "mere fact that" would justify the rejection of any counterclaim. Consider if you will: "The mere fact that Italki Forum Member Blodger Bulldoo wrote his reply in a much calmer tone, served to show that his thinking was more reasonable than the thinking of his critics." "The mere fact that he wrote with a calm spirit, certainly serves to show something!" "The mere fact that the people of Hong Kong conduct a nonviolent protest, serves to show that their call for a democratic election is a reasonable idea." .

"The mere fact that several people have responded to your question shows that people do care about your pursuit of knowledge." "The mere fact that the person shared several relevant book titles with you shows that he knew something about this subject." "The mere fact that your roommate loaned you some money in your moment of need certainly shows that he cares about your difficulty." "The mere fact that your roommates invited you to dinner shows that they care about you. "The mere fact that she thinks about the problems of others more than her own difficulties shows her to be an altruistic and charitable young lady."

a simple fact means something, and you use the phrase, for example: the simple fact of you being here, is that your boyfriend is too.

It means the 'very' fact... The mere fact that she agreed to help us is a good sign. (Just the fact that she agreed to help us... ) Hope this helps.