“Reading” here is basically a translation of 読み, which in a kanji-studying context essentially means 読み仮名, so it’s the kana that represent the reading, and so you can have identical pronunciations that are wrong just for spelling reasons.
For instance, when お sounds are lengthened, お or う can be used, usually differing based on etymology. They result in identical pronunciations of lengthened お sounds, but one or the other is correct, and the opposite is wrong.
Similar things can happen with づ/ず and ぢ/じ.
びーだま is not standard, for sure, but there’s no rule that a lengthener symbol can’t be used with hiragana. It’s just uncommon. For instance you’ll sometimes see ramen spelled らーめん.