(a) How do the hens know there is a river separating them from the rooster?
(b) Also: What is the hava amina that not checking well enough might get you a heter to eat the egg you found?
(a) It seems that the hens are free to walk about (as the Gemara later says on 24a). When they hear the crow of the rooster, they hop in its direction, but when confronted by the river they do not cross to meet the rooster.
(b) When one did not check for an egg on Erev Yom Tov and then finds an egg at dawn on Yom Tov, we follow the nature of most eggs, which are laid during the day. Therefore, we assume that the egg that he found was laid the day before, and not during the night of Yom Tov. Even had he checked earlier, he would have found that the egg was laid before Yom Tov, by day.
You misunderstood my question, I think. The gemara suggests that maybe one checked, but didn't check well enough, but somehow thinks a leniency is ok here. Since when do we apply such an idea!?
If one did not check well enough, then certainly there is room for leniency, based on the principle that a hen (in the area of a rooster) lays egg only by day. Since the case is referring to when the hen had access to a rooster, and we know that an egg formed from such a union is always laid during the day, then even if he checked before Yom Tov and claims that there was no egg there and that it must have been laid at night (on Yom Tov), we do not rely on his word in this regard, because it is not possible that the egg was laid at night. Instead we assume that he did not check thoroughly (or that it came out during the day and went back in).