On page 5 in the road to legend rulebook it says:

INTERACTING WITH THE MAP
Heroes can examine any element of the map (like a door or token) at any
time by selecting it in the app. Selecting these often provides information
about the token as well as how the hero can interact with it on the game
board.

A hero figure does not need to be adjacent to the particular element in
order for a player to examine it.

Does this mean that heroes can open doors etc. from anywhere on the map, i.e. not only while adjacent to those, or simply that they can click on them to view any relevant information regarding that element while not being adjacent?

No, it means that you as the player could click on a element of the map to EXAMINE IT. So if there is a banner represented by a objective token, you can "click" it and it'll say "this is a banner, you may test might or willpower to remove it from the map." But you can't actually do the test until you're adjacent.