ORA-06550/PLS-00201 Because Procedure Executing Against Wrong Connection (4244262)

The 'Execute Procedure' icon in the Schema Browser of TOAD is executing against the wrong database connection and thereby failing with the following error:

ORA-06550: line 10, column 13:
PLS-00201: identifier 'PACKAGE.PROCEDURE' must be declared
ORA-06550: line 10, column 3:
PL/SQL: Statement ignored

Steps to Replicate:
1) Create these 2 objects in 2 schemas on 2 different databases of different version numbers.

CREATE TABLE TEST_STATS(FLD VARCHAR2(100)) ;

CREATE OR REPLACE PROCEDURE Gather_Stats AS
s VARCHAR(100);
BEGIN
SELECT VERSION INTO s FROM SYS.PRODUCT_COMPONENT_VERSION WHERE UPPER (PRODUCT) LIKE '%ORACLE%';
INSERT INTO TEST_STATS VALUES(s);
COMMIT;
END;
/

2) Go to a Schema Browser and execute the procedure.
3) Change the session to the second schema and execute once more.
4) View the table data for both schemas. 1 schema will have incorrectly gotten both of the insert's where as the other didn't.

The Schema Browser will always fail with this case. If using the debugger module, the Procedure Editor lightening bolt will work, but right click "Execute without Debugging" will not. If not using the debugger module, the lightening bolt in the PE will execute in wrong schema as well. Executing via the Project Manager will fail as well.