On slaughtering the red heifer "outside of the pit" has to mean more than "outside of the Temple," as this offering was always made outside of the Temple. So what is the concern here? The Gemara provides a few suggestions. Also, a sidestep away from the dispute between R. Yochanan and Resh Lakish on the daf about the concern of impurity in the land - and whether there might be bones in the ground from the time of the Flood (which, if there, are reason to be concerned about impurity in the ground). But did the Flood actually come to the land of Israel? And could there be anything interfering with the (apparently identifiable) bedrock? Plus, women would give birth to children who would draw water to contribute to the next red heifer offering (as part of the process) - children who were kept free of ritual impurity to be able to play this role. And if that isn't clear for the whole land, then at least Jerusalem - where R. Yehoshua essentially stipulates that the holy city is not impure. Also, more on the Flood itself - and how the huge animals were saved from the waters, given that they wouldn't have fit on the ark.