You can swap "very minimum" for "minimum". The "very minimum" means "the extreme minimum" or the "true minimum". Well, a minimum is already an extreme; and absent reasons for believing otherwise, it's reasonable to assume that a speaker wants you to believe she is truthful.
You can use "very" simply for emphasis, rather like "literally" is often used; "I did my very best". If it's really being used just for emphasis, then you can delete the word "very", and simply set the following word in bold or somethiing.
You can use "very" simply for emphasis, rather like "literally" is often used; "I did my very best". If it's really being used just for emphasis, then you can delete the word "very", and simply set the following word in bold or somethiing.