Originally Posted by Often1

No. Air travel is not the same thing as hotels/cars. With air travel, you can wind up buying walk-up fare on next flight at many times your original cost. With hotel/car, even when they are prepaid, worst case is that you lose the value of one night in the hotel or car for a day, although even that would be unusual (so long as you keep the hotel/rental company updated).

The point here is that booking separate tickets alleviates the originating carrier of any responsibility for getting you beyond your destination which, in their case is actually the location you choose to connect. If you buy: AAA-BBB-CCC and buy two tickets: AAA-BBB and BBB-CCC, so far as the first carrier is concerned, they got you to BBB.

Online booking is convenient and easy (generally), but particularly interline and international and without carefully reading the Contract of Carriage for both carriers, it's well worth paying the telephone fee and better yet, a TA.