U.S. Customs and Border Protection (CBP) agents are allowed to go through the documents and ask you questions about them, under practically any circumstances, even without suspicion of any criminal activity. The question of if there is a "reasonable chance" they will do so is mostly at the discretion of the agent you encounter and often times, in the agency's own words, "completely random" (see the bolded statement in section quoted below).
CBP provides an explanation of this authority and additional guidance they issue to agents on their public website at https://www.cbp.gov/travel/cbp-search-authority.
A U.S. Customs and Border Protection (CBP) officer's border search authority is derived from federal statutes and regulations, including 19 C.F.R. 162.6, which states that, "All persons, baggage and merchandise arriving in the Customs territory of the United States from places outside thereof are liable to inspection by a CBP officer." Unless exempt by diplomatic status, all persons entering the United States, including U.S. citizens, are subject to examination and search by CBP officers.
CBP Officers use diverse factors to refer individuals for targeted examinations and there are instances when our best judgments prove to be unfounded. Although CBP does use information from various systems and specific techniques for selecting passengers for targeted examinations, a component of our risk management practices is the use of a completely random referral for a percentage of travelers.
Within the related link on the above page to "U.S. Customs and Border Protection Policy Regarding Search of Information" you can find the guidance agents use in regards to search, seizure, and additional handling of information in documents and electronic devices.
B. Review of Information in the Course of Border Search
Border searches must be performed by an officer or otherwise properly
authorized officer with border search authority, such as an ICE
Special Agent. In the course of a border search, and absent
individualized suspicion, officers can review and analyze the
information transported by any individual attempting to enter,
reenter, depart, pass through, or reside in the United States,
subject to the requirements and limitations provided herein. Nothing
in this policy limits the authority of an officer to make written
notes or reports or to document impressions relating to a border
C. Detention and Review in Continuation of Border Search
(1) Detention and Review by Officers. Officers may detain documents and
electronic devices, or copies thereof, for a reasonable period of
time to perform a thorough border search. The search may take place
on-site or at an off-site location. Except as noted in section D
below, if after reviewing the information there is not probable
cause to seize it, any copies of the information must be destroyed.
All actions surrounding the detention will be documented by the
officer and certified by the Supervisor.
Section D of that document outlines the reasons information/devices may be kept and includes: "Retention with Probable Cause", "Other Circumstances" (i.e. items specifically related to customs and immigration but not criminal), "Sharing", and "Destruction"
If the documents don't meet any of the criteria for retention/review, they should not be taken from you or retained by the agency.
Also worth noting, there are special handling instructions for certain types of documents: "business information", "sealed letter class mail" (you may know it as first class/registered mail but it must be transiting the postal system - not in possession of an individual/parcel service - to qualify for special handling), "attorney-client privileged material", and "identification documents". In regards to this specific question though, there seems to be no such special instructions for medical information.