Here is the deal about Singapore. Immigration will stamp a 4 day temporary permit on your way to India if you have an Indian passport as your destination is your home country and the country cannot refuse entry to its citizen.
But, if you are planning for doing it on your way back to US, they will not stamp or let you out of the airport. They would do that if you have a valid US visa but for AP, they do not. The reason the Singapore IO gave is the destination country could refuse entry and the person becomes a burden of state on the port he/she started from which would be Singapore and eventually they have to remove them and bear the cost.