My dad had his share of entirely real weird stories, which isn't that surprising I guess given his career as a musician, along with various side jobs and travelling experiences.
We used to live just outside a big 4-star hotel in Russia, so when things were really bad (financially) in the early 90's, my dad would just go out in front of the hotel and play for the tourists. Once he was approached by a Korean guy who wanted him to play "rock and roll". Dad played him some Elvis song; the guy opens his wallet, looks in, and there's only $100 bills in there. So he thinks for a moment, then gives him an $100 bill and again says "rock and roll". Dad, confused, plays the exact same song again, for which the Korean visitor promptly hands him another $100 bill and leaves. In the early 90's, I think we could live a couple of months onhe pay from that "rock and roll" incident
There also happened to be a conference of European mayors at that hotel, and dad once sighted a group of them talking outside, in French as it turned out, and promptly got to playing in front of them. They indeed turned out to be French mayors and he talked to the mayors of Lyon and Paris (in English) for several minutes, with them mostly wondering what life is like in Russia. Now, the mayor of Paris at that time was none other than Jaques Chirac, the recently-departed French president.
And that wasn't the end of his presidential encounters; in 1994 he went to the St. Petersburg city hall with some paperwork to register my grandmother's small business. A short, gloomy-looking city official signed off on their papers - none other than Vladimir Putin (who indeed held various posts at the city hall until his sudden rise late in the 90s).
So, morale of the story: if you meet my dad, there's a good chance you'll be president in few years.
There's also the story of my dad's first tour of the US in 1995. When he was in Phoenix, one of the people he knew there offered him a lift and invited him to come along and get something to eat with him. It was getting late however, and dad figured he'd better go to the place he was staying. So, the guy dropped him off and headed to the nearest food place by himself - but didn't get very far, as at the very next corner a truck plowed into the right side of his car, totally demolishing the passenger seat (though the driver walked away). Lucky escape there, and I guess that may be one reason my dad doesn't like fast food