Access, as a noun, has been established since the fourteenth century. It means the ability or permission to enter or go through an area or communicate with a person. One would gain access or have access to something.
As a verb, however, access has only been around since the 1960s. It has almost the same meaning as the noun form, to gain access to something or someone. It does also mean specifically to load or open something digitally. We presume its origin and rise in popularity are tied to the increase of technology as well.
Some may consider access to still be relegated to the noun category, but it is perfectly acceptable to use it as a verb. If in doubt, however, one could simply use a synonym.