Is what some people claim true or false, that they possess blessing for treating illnesses by blowing on a string or water and presenting it to the patient, or for treating rabid animals?

Blessing is not affirmed for anything or anyone except with proof. There is no harm in performing ruqyah by reciting over water or oil and giving it to the sick person to drink or anointing them with it, or by reciting directly over the sick person or over an animal. The Pious Predecessors, including the Companions and their Successors, did this. As for reciting over a thread and tying it or hanging it on the sick person, this is not permissible. This is the view of those who forbade hanging amulets, even if they were from the Quran.