The gemara explains that acc. to r' eliezer we use a straw for parah adumah that chazal were gozer should have status of tumas meis which would normally require h'erev shemesh, yet we use it as a tvul yom, and this it motzi m'liban shel tzdokim. The difficulty is that if you would ask the tzedokim they would also tell you that this straw can be used without he'erev shemesh, bec. the entire source of tumah is purely rabbinic (to treat the straw as tomei meis) which they certainly don't hold of. So, how is this motzi miliban shel tzdokim since the tzdokim themselves hold it can be used?
We learn from here that being motzi milban shel tzedokim does not mean that we show the tzedokim that we use something that they would not allow. Rather, we pay no attention to the actual opinion of the tzedokim. Our concern is that some perushim may give some credence to the tzedoki "chumras" so we use a straw that under perushim rules should require h'erev shemesh, to show that we disregard even the chumras of the tzedokim. Tosfaos d.h. metamin, points out that even acc. to R' Yehoshua where we are actually metamei the straw, we also use a type of tumah not recognized by the tzedokim. Tosafos clearly says that the motzi miliban is for US, not for THEM!