Words have meanings and in this case the semantics count. It's not what you and I call it or think it is that counts. It's the words ATC uses that count.I think you all know the requirements of entering the various controlled airspace and are simply arguing the semantics of whether those requirements amount to a "clearance".
You: a clearance is something that you request and are explicitly given.
Them: a clearance is implicit when you meet the requirements for entering the airspace.
implicit vs explicit is what you're arguing. Call it what you like as long as you know the requirements.
You have a clearance when the word "cleared" is used.
You are VFR and are speaking with the tower at a Class D airport. Both your and they are using your tail number in the conversation. You may enter the Class D airspace unless instructed to remain clear. Not one more singe word is required. The word "clearance" never needs to be said or heard. But that conversation does not mean you are cleared to land until those words are heard. Same is true for Class C.
Class B? Different story.
First, you question whether the vector providing the heading and altitude assignment is a clearance under § 91.131(a)(1) to enter the Los Angeles Class B airspace. The answer is no. A pilot must specifically receive an ATC clearance to enter the class B airspace. The issuance of a vector provides navigation information but does not provide clearance from ATC to enter the subject airspace. 2010 Doremire interpretation.
You are VFR and speaking with Approach for the Class B airspace. Both you and they are using your tail number in the conversation. They may even have given you a recent vector for traffic that puts you on a direct route to their airspace and kind of forgot to tell you to "resume own navigation." You have not been instructed to remain clear. You enter the Class B airspace. You have violated the reg.
We have "terms of art" aka lingo aka jargon in aviation. Understanding the lingo is an aid to understanding the underlying concepts.