Parah, Chapter 2, Mishnah 4. This chapter examines what disqualifies a cow from serving as a parah adumah, and among the disqualifications is anything that amounts to the cow having been put to work or otherwise used. Our Mishnah takes up two borderline cases where something happened to the cow without the owner lifting a finger.
A bird that rested on it
Take the first case. "Shachan aleha of" - a bird came down and perched on her - and the halachah is "ksherah," the animal remains valid for use as a parah adumah.
Why should this be obvious? Because a bird alighting on a cow brings its owner no satisfaction whatsoever. Nobody gains anything from it. We learn the measure here from the eglah arufah: where an act done with the animal gives the owner no gratification, it is not counted as use of the animal, and it does not disqualify it.
A male that mounted it
The second case turns out differently. "Alah aleha zachar" - a male beast climbed onto her - and here the ruling is "psulah," the animal can no longer serve.
Coupling of this sort is treated as work done with the animal. Now one might have argued that here too the owner gains nothing, since in the case of a parah adumah he certainly does not want this to happen; on the contrary, it displeases him. Nevertheless the cow is unfit. The reason is that we do not judge the matter by this particular owner's momentary feelings. With cows generally, owners are pleased when a male mounts them, and the parah adumah is assessed according to what an owner would ordinarily wish for. Moreover, consider the practical consequence: were we to declare the cow fit even after such an occurrence, the owner would happily welcome the male's mounting, having nothing to lose by it. And that welcome itself is precisely what renders the cow unfit.
Rebbi Yehudah's distinction
Rebbi Yehudah qualifies this ruling. "Im he'elahu" - should the owner have hoisted the male onto her - "psulah"; "ve'im me'atzmo" - whereas if the male came up under its own initiative - "ksherah." Everything turns, in his view, on whether a human hand was behind the act. An owner who raised the male up, or steered it toward the cow, has forfeited her. An animal that climbed up entirely by itself, with no prompting or luring from the owner, leaves her fit.
For Rebbi Yehudah, then, the disqualification is not limited to a case where the owner physically caused the coupling. It extends to any case where the mounting was something the owner welcomed. Where it was genuinely unwelcome and the animal acted of its own accord, the cow keeps its fitness for the avodah of the parah adumah.