Yes, you’re absolutely right. They are, as we say, alleging something in contrast to stating something as a fact. It is a form adopted by reporters, newspapers to protect themselves in case the ‘allegation’ turns out to be false. It is also often used by sensation-seeking newspapers which can allege something, get public interest, sell newspapers and then if it is without foundation, they are not involved in any compensation.
As I understand the two Prime Minister (PM) sentences, the second one implies that the PM did not get involved himself; someone else involved him, with or without his consent, true or false. The first sentence implies that the PM acted to be involved.
Not wanting to hijack the thread, may I ask a question?
What if instead of WAS in the first sentence, the verb was IS, reading “It is said that the Prime Minister IS involved in a drug scandal”?
Similarly, what if instead of HAVE BEEN in the second sentence, the verb was BE, reading “The Prime Minister is said to BE involved in a drug scandal”?
Both are merely supposition. It isn’t clear whether the information/supposition is true or not. Changing from 'was to ‘is’ and changing to ‘be’ merely makes the suppostion actual (of now).