Trump said, "They gave me a disease". I think he was throwing the water to the ground as if it was tainted.
Just looked at the transcript, and you are right- he said "another disease". Maybe it refers to whatever was hidden in the White House walls, some thought could have been emitting radiation:
"VA recognizes that the following diseases are possibly caused by exposure to ionizing radiation during service:
-All cancers
-Non-malignant thyroid nodular disease
-Parathyroid adenoma
-Posterior subcapsular cataracts
-Tumors of the brain and central nervous system
publichealth.va.gov/exposures/radiation/diseases.asp