what edwinbear said! god she is 3 give the poor child a break! i would be asking the nursery what the circumstances were that led to them telling her not to suck her thumb ie painting, cooking etc, then yes explain its not appropriate to suck her thumb at that time.
the dentists i have spoken to say its not a problem until adult teeth start to come trhough, my ds4 is just 4 and sucks his thumb, pretty much only at bedtime and when tired/poorly, sometimes when watching tv. he doesnt try to talk with it in his mouth and his speech is very good, it hasnt affected his teeth in anyway and he hasnt had tummy bugs etc any more than my other childrne who werent thumb suckers, two of my children bfed till almost 4yrs so its the same thing really a comfort! he did it lots as a tiny baby, did it in utero (scan pics) and as he has got older has done it less, going through phases if ill or in a developmental phase etc.
i dont think my ds4 sucks his thumb at pre-school as generally he is too busy, tho if tired and he has a rest then i imagine he would do,t hey ahve never mentioned it tho.
if the nursery had an issue with it then they should raise it with the parents.
oh and ds4s thumb and hand doesnt get all wet and slobbery, maybe a tiny bit damp but its certainly not as wet and disgusting as some here have made it out to be! babies and children can be slobbery and they dribble etc, a little bit of saliva isnt an issue generally given everything else that children get up to, sharing food, drink etc.