You are correct depending on the terminal. The example I was giving was if you had to connect in Singapore to one of the budget airlines like Tigerairways or CebuAir to another international desitnation (we were flying from Thailand to Darwin Australia via Singapore). This is a different terminal (Terminal B) than the main terminals (T1,T2,T3) and they make you go through immigration first before transit even though it is the same airport and it is an international flight. For for T1,T2,T3 you do not have to go through immigration but if you arrive in T1, T2, T3 and have to transit to Terminal B then you have to go through immigration. This is what happened to us.
Sorry for over generalizing Singapore airport.
More info from their webiste:
"(b) If you are connecting to or from a budget airline flight :
As budget airlines do not have transfer counters in the Transit Hall, you have to ensure that you have the valid travel documents (passport, visa etc) into to clear Customs and Immigration into Singapore. You have to collect your baggage and check-in again at the Departure Hall of your connecting flight.
If you are connecting to Tiger Airways or Cebu Pacific Air, please proceed to Terminal 2 Basement to catch the free shuttle service to the Budget Terminal. You may visit the Budget Terminal website for further information.
For the location of our transfer counters, you can see our Inter-Terminal Transfer Map.
Another example would be Kinabalu,, Malaysia. On a flight from the Philipines to Kinabalu, Malaysia, we had to go through immigration before we could get on a flight to Bangkok. Pretty small airport though.