The button to Infiltrate a city isn't greyed out when the Great Spy is in the player's cities. If you accidentally click it, the GS will, in fact, "Infiltrate" your own city - which is completely useless, obviously. The game does have text indicating that Infiltration can only take place in foreign cities, but doesn't seem to stop it locally.
To reproduce this bug:
1) Start a new game
2) Build your starting city
3) Open up the Worldbuilder and place a Great Spy in your new city
4) Click on the "Infiltrate Player's City" button
Bh
To reproduce this bug:
1) Start a new game
2) Build your starting city
3) Open up the Worldbuilder and place a Great Spy in your new city
4) Click on the "Infiltrate Player's City" button
Bh