Allegedly marks 'people say this is true, though it has not been proved.' It sits beside the doubtful part: he allegedly took the files; the river was allegedly poisoned. News uses it to report a claim and stay safe; speakers also use it with a raised eyebrow, as if to say 'so they say.' It does not mean 'probably,' and it does not mean 'definitely.' It only marks the gap between talk and proof. In print it feels formal; in speech it can sound careful or a little sharp. Though actually, readers often skip the word and still hear a fact — which is why writers put it there.