Does the existance of interline baggage agreement matter, if the tickets are bought separately?

Hi There, I reviewed a couple of answer/questions, but still a bit confused on the interline baggage agreement. I have two separately bought tickets from Delta and Alitalia, and on the way back from Europe to US, I would like to make sure that my baggage goes through at Frankfurt airport where I change my... show more Hi There,

I reviewed a couple of answer/questions, but still a bit confused on the interline baggage agreement. I have two separately bought tickets from Delta and Alitalia, and on the way back from Europe to US, I would like to make sure that my baggage goes through at Frankfurt airport where I change my flight.

The general consensus from the answers is that, if there is Interline baggage agreement between those two airlines (which Delta and Alitalia do), my baggage goes through at Frankfurt. However, does this also really apply to two tickets bought separately? I called about several times to both airlines, but I have about dozen various answers. Could any exparts assure me that the interline baggage agreement is still valid for a travelor like myself?
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