There was a big case from the Missouri Court of Appeals last year that went into great detail on what was allowed and what wasn't in seeking informal discovery from a plaintiff's health-care providers. Today, the Supreme Court issued it's opinion in that case.
Here's the relevant part of the opinion:
The rules of discovery enumerated by this Court are found at Rules 56 to 61. These rules provide the trial court discretion to issue orders relating to the perimeters of interrogatories, depositions, production of documents, requests for admission, physical and mental examinations, and discovery sanctions. The defense in this case concedes that there is no discoverable information that they could obtain from an informal ex parte discussion with the treating physician that they could not obtain by use of these rules of discovery. However, there is nothing in these rules of discovery that authorizes the trial court to issue orders governing methods of informal ex parte communications with plaintiff's non-party treating physicians.