I think you are absolutely right to be ticked off.
I can understand how some parents might be a little lax, if maybe they have been in the waiting area for a long time already and have sortof run out of threats already.... Sometimes bringing a child along isn't really an option, but just a necessity/reality of life. The kids know that mom has no choice, and they are bored and their patience is gone after 45 minutes in a dull waiting room. Don't misunderstand, I am not saying it is ok.... just looking at it from a slightly different perspective.
I tend to be over concerned that my kids might mess with something they shouldn't, and many times have had someone tell them "oh it's okay, you can ____" after I've told them not to ____. As a parent, it can be awkward too, b/c interrupting the doctor/client discussion to correct the child can come across as rude, as well. I've felt very rude in the past, for correcting my child, when an adult was talking to me. However, my kids are a little older now, and guess what? I don't have to make all those corrections anymore--most of the time. And when I do, it is almost ALWAYS because we have been sitting W-A-I-T-I-N-G to be seen.
I know that isn't your fault, and the parents you had as clients know that, too (I hope), but it doesn't make their child's patience last longer just because they know that.
I LOVE the suggestion to speak directly to the child (and indirectly to the parent) that you would "hate for your mom/dad to have to buy me a new computer/keyboard/stethoscope/otoscope/_____." You could even include that "THAT one only cost me about $_____, but I think they've gone up since then...."
But you could also say something like "The office rules are that only staff handle ____." Perhaps you could dig up some sort of insurance/liability issue to blame it on?