No, not really, because actually when you have this much contact after YOU are saying they told you that you were fired, it looks more and more like they actually accepted a resignation. The other employee could very well testify (if he were interested in keeping his new general manager job) that you walked in and told
him you were quitting. All this blah blah blah paper trail isn't necessary, and does make it seem more like it's your idea or that you have felt no qualms about continuing to stay in touch with the company owner after he supposedly fired you third hand.
When you are fired, you are usually told to leave the workplace and barred from coming around. If the guy had shown up at this place of business again at his regular work time, they very well might've called and had him removed by the police, which would've been a nasty scene all around. I think he did the right thing to just leave, attempt to contact the owner, and then assume he was fired.
You say you might think a responsible business owner would at least give the guy a letter....or something. Well, I sort of had delusions about this sort of thing until, in the later part of my career, I began to work with employers instead of claimants. I never met such a group of thoroughly irresponsible, mean spirited, oh well.....there were
some nice ones.

But trust me, I have seen many cases where people worked and came into work one morning and found the doors locked and the owner swooped, owing the last month's wages, too. I have seen people fired and then an entire personnel file full of warnings and reprimands manufactured to fit the termination. I could go on and on.
And the unemployment investigator who's making the decision here isn't going to make this a CSI case. Anybody can fake papers and letters they supposedly wrote to the employer, employee, etc. Those types of paper trails have very little weight. And yes, it would be nice if an employer always felt it mandatory to give a terminated employee a letter or separation notice. Some do. A whole lot do not. And even in states like mine, where it is supposed to be a law that the employer is to give you a separation notice within a certain amount of time after you are terminated, this law is useless, has no teeth in it, and if you waste a lot of time trying to get a separation notice discussing cause before you file a claim for unemployment, you sometimes miss weeks of benefits, because they won't usually let you backdate, it only starts paying for weeks after when you have filed it. He should go on and file his claim for unemployment, not wait for a letter. They'll shake it all out.