Mishnayos Parah Perek 2 Mishnah 4

עלה עליה זכר פסולה – even though it is not what it prefers, because its costs are expensive and [the owner) loses a lot, and regarding the work it is not what he prefers it does not invalidate it, as it written regarding the heifer whose neck is broken (Deuteronomy 21;3); “a heifer which has never been worked, it is written as עבד – but it is read as עובד. Just as עבד is preferable to him, even עובד is preferable to him, and we derive the sin-offering of the heifer from it. Nevertheless, since that with the rest of the cows it was preferable to him (i.e., the owner), we consider that regarding the sin-offering of the heifer is also preferable to him (i.e., the owner). And further, if you came to validate it, if so, it is also preferable to him (i.e., the owner), and because of this it is invalidated.

העלהו פסולה – Not exactly “brought it up” [upon the cow], but rather, if it went up upon her (i.e. the cow) with the knowledge of the owners, even if it went up on its own, it is invalid. But if it went up [on the cow] without the knowledge of the owners, it is fit/appropriate. But the Halakha is not according to Rabbi Yehuda.