Hi wendy, the difference between cleaning gravestones and cleaning historic pictures is that one would hope that the person cleaning the historic pictures would be trained and qualified to know exactly what they are doing, what materials they are dealing with, and the ramifications of the treatment they are undertaking!!
Having said that though, I recently went to an old cemetery in the UK and found the gravestone of my ancestors' plot fallen on its face. With a couple of cousins I lifted the stone so we could read the face of it (most of which had rotted away - cheap stone

) ... if it had not been almost completely deteriorated as it was, we would have put it back face down, where it would have been protected. But as we are the only descendants of those in the grave, and the stone was almost destroyed (or at least the text) we left it up.
I think as long as you understand the consequences of what you are doing, you should be allowed to clear around, and clean off to a certain extent, gravestones that are relevant to you. Be aware that lichens, moss and overhanging greenery can help to protect the stone; that sometimes the lichen and moss are actually helping to hold some less stable stones together and if you remove them the stone may fall apart in front of your eyes; that if you scrub at a stone you may end up with the same result; and then proceed!
I have heard of people using chalk, or crayon over thin paper, to rub gently over a stone to read the letters - not sure how effective this is? Might not have to do so much cleaning then...also with digital cameras and software being what they are today, often a photograph can be manipulated to show alot of detail.
Sorry for the mind dump

Prue