I hope you are joking...
No, I'm very, very serious about all this.
Sorry, but I don't buy into the campaign of misinformation that's been perpetrated on the unsuspecting American public for the last couple of hundred years. American people always joke about the incestuous nature of the British royal family, but if they only knew how much worse it was in their own country, surely they would revolt. So that's why The Powers That Be have gone to such great length over the years to keep things under wraps.
For example, FDR was, without a doubt, TR's bastard son from an out-of-wedlock relationship he had maintained with a Boston prostitute. If news of this had gotten out, surely it would have caused irreparable harm to TR's burgeoning career in the New York state legislature, so it was decided that the bastard child Franklin would be sent to live with TR's distant relatives upstate.
Years later, as FDR was developing quite the political career of his own, his lineage and relationship to Theodore, whose recent death some historians believe Franklin may have had a hand in, started to come into question. To stifle this, FDR's people came up with a plan: Poliomyelitis, better known as polio. FDR "mysteriously" contracted the disease while vacationing in Canada. And their ruse was successful on two fronts. Not only were all of the "FDR is the bastard child of TR" rumors effectively and immediately quashed, as surely this crippled, decrepit man could not have come from the loins of such an active and vivacious man as TR had been, but FDR and his people used his "disease" to play on the sympathies of the American voters, who voted him into office just a decade later. And FDR kept up the polio act, whenever in the public eye, up until his death, but as White House insiders would tell you (if they were still alive), in secret, FDR was, just like his real father, quite the sportsman, enjoying basketball and bowling at nearly every opportunity.
The Andrew Johnson/Lyndon Johnson connection (or "Johnson & Johnson," as it's come to be known in historian circles) is a much-less sordid tale than that of the Roosevelts, but no less interesting. Yes, it's true that Andrew Johnson died over thirty years before Lyndon Johnson was born. That's common knowledge. Irrefutable. What most people don't know (and what most historians won't tell you) is that Andrew Johnson was indeed the biological father of Lyndon. How can that be possible, you ask? Simple. After Andrew Johnson died in 1875, his body was sent to a local mortuary, where a young mortician on an apprenticeship was getting his first crack at a "real live body." Unobserved by his mentor, and slightly intoxicated and delusional from the moonshine he had been making in the funeral home's bathtub, the young apprentice decided he would try out a few of his radical new "embalming techniques," one of which included obtaining a sperm sample from the deceased.
The rest of the story is far too complicated and boring to go into great detail on here, but, rest assured, that little did the budding apprentice know at the time that his bizarre experiments that night would later lead to what is now considered to be the first, albeit unofficial and undocumented, successful case of artificial insemination in humans.
Now, how that little seed eventually grew up to be president--in much the same way his father did--well, that's a story that's best left for another time. However, with Lady Bird Johnson's recent passing, don't be too surprised to see the bodies of both former presidents exhumed in the near future for extensive DNA sampling, to finally set this nearly-unbelievable tale straight.
By the way, don't look for any of this stuff in the history books, 'cause it's not there. But maybe one day, the truth will come out, to vindicate the true historians, and to shut the naysayers up for good.