In our current game, the Grave Robber landed on the Graveyard space, which had a face-up enemy card on it (I forgot how it got there)

The player using the Grave Robber said that his special ability (picking 8 Adventure Cards looking for objects) should trigger regardless of the outcome of the battle, because the Graveyard had been visited - it was where the battle occured.

Other players argued that the Grave Robber must first defeat the enemy before he can encounter the board (and only then encounter / visit the Graveyard).

I'm torn. The second option seems more consistent with basic Talisman rules - but I can symathize with the Grave Robber that it seems wrong that he can't use a special ability as printed on his card.

Any thoughts?

Well.. according to the rules he must fight the enemy before encountering the space (cards on other spaces than draw-card-spaces).

According to the very same rules the characters turn -ends immediately- if the outcome of the battle is defeat or standoff.

So.. no cards for him

yep that's right you must encounter everything on your space before visiting the space.

Rule Book, page 10:

Characters must follow the instructions on the space if their player chooses to encounter the space instead of encountering another character. However, before they do, any Enemies in the space must first be killed (see “Resolving Battles vs. Creatures” on page 10) or evaded (see “Evading” on page 14). Any Stranger or Place there must be visited and any gold, Objects, and Followers may be taken.

And from the section "Resolving Battles vs. Creatures":

If the character is defeated or the battle ends in a stand-off, the character’s turn then immediately ends.

So any cards that are there must be resolved first. Then and only then may the space be visited. Think of it in terms of all of those cards standing at the gate. You must get through them in order to get in.