We know for a fact that meteorites on earth have originated on Mars. Theoretical calculations show the trip in the other direction, while less common, would happen. So cross-pollination is possible.
The mistake I see in what you mention about sterilization is that sterilization is not required.
What is required is that they be different. So, for example, we might put 12 sealed containers on a satellite. Open three on mars to culture leaving the other 6 sealed. Then, after some reasonable period of time ... compare their contents.
If the six that were opened contain some life form not present in the six that were not opened ... you have strong and convincing evidence that what is growing in them is living on Mars.
I think we can test/falsify the proposition with relative ease. I suspect the real question is one of political will. Because, as you state, the implications are enormous. Where, for example, would the earth's religions be if we actually met little green men and they laughed at our quaint stories about Moses, Jesus, and Mohammed.
