From my experience going round (dragged round) graveyards by Sarah:
If a gravestone from a glance definately is not the right one, obviously I would leave it alone.
If details are obscured then I would pull back any grass, or ivy to try and see the detail.
If I thought in any way that the grave could be damaged by my action, then I wouldn't disturb it. Also in the same manner, after disturbing any ivy or grass then I'd lay it back on. God's a better garderner than me, and knows best.

In cleaning a grave, whether it be my relative or not, it gives a great moment of thought, reflection and respect for that person that was laid there, to think that somebody loved them enough to lay a stone for them, and for one moment to imagine their personality.
Don't tell Sarah, but I love grave hunting with her!
Trystan