Yes there is, the fact that we see page after page of a pre-dip Joker struggling as a no named Joe, whether that's intended to be a real flashback or imagine. That's entirely up to the viewer. There are like 10 pages showing what happened to him, and just one little panel that suggests that it varies from time to time. Let's remember, he also states that line to Batman. The Joker is a liar. One minute the character thinks this way, the next another. So who knows. The Joker wouldn't tell Batman the truth, why would he? It'd make him vulnerable.
I think (I think) the whole flashback after he's looking all sad in his reflection at the carnival is true. He had a pregnant wife, he was a ****** comedian, some guys tricked him into the Red Hood gig, he ran into Batman, and fell into the chemicals. All the events of that day/week drove him mad. Didn't Alan Moore even say that's what he intended? Those that think it's true aren't interpreting it wrong and vice versa.
That was his "bad day". The day he tried to give to Gordon. The day Batman had when he was a child.
Of course, the Joker being as crazy as he is might have put that in the back of his head and forgot who he really is. Or maybe he wants to try and impress Batman with his insanity like "HEY MAN, LOOK HOW CRAZY I AM, I DON'T EVEN KNOW WHAT I WAS BEFORE THIS". Who knows.
Point is, there's nothing definitive from story to story. Writers write what they want and fans interpret it how they will.
The Joker is Jack Napier, the mob hood that's dropped into a vat of chemicals by Batman. The Joker was the Red Hood, he was dropped into the chemicals by Batman. The Joker was a guy that suffered from a persona trauma from his scarring and was inspired by Batman. The Joker has an origin story. The Joker doesn't have an origin story. The Joker has bleached skin. The Joker puts on make up.
All these things above are true.
With thousands of stories out there written by all sorts of different creative minds, nothing is definitive. That's it really, origin or not.
If I'm going to have a favorite Joker interpretation, I prefer it to be multiple choice. Whether his origin is real or made up, whether he's bleached or puts on make up.