Reb E, a sotah did an aveirah that is not in doubt. She has, to some degree, lost her chezkas kashrus because of yichud. That’s because the halacha follows rebbe Yehoshuah who holds in sotah 2a that we need 2 aidim for the warning and for the yichud. The tanna that shares your name, rebbe Eliezer, holds that one aid is enough for yichud (or even the husband himself seeing it) – maybe you’re shayach to his shoresh neshoma so your mind is going leshitaso, but lehalacha we need to establish some guilt of the sotah before trying her with the water.
In the case of an accused abuser, often there’s absolutely no raglayim ledavar, suspicious behavior, multiple accusations, or other indication… I have no idea how common it is for kids to make up stories, but i will say that as a rebbe I’ve heard kids half-threaten to accuse teachers including myself of abuse in order to het what they want or for revenge for a perceived injustice. I know lf at least 2 confirmed cases of this happening elsewhere.