You have a false dichotomy between "birtherism" and "trutherism." "Trutherism" isn't a real movement because they don't care about the truth; It's all about the fishing expedition you describe to get as much dirt on the other side. Really, they're all a waste of time until one side uses it to slander his opponent.
"Birtherism" is just a name for a bunch of idiots to rail against everything: "socialism," homosexuality, etc. There is a valid argument that McCain wasn't native-born (since he was born in the Panama Canal Zone to active-duty parents), but there was no one seriously doubting it. In fact, in the 2008 elections, people even discussed amending the law so that there would be no question McCain qualified to be president. That's not the same as the nutjobs who still think Obama was born in Kenya, Indonesia, or somewhere else. Nearly every single Republican candidate believes in "birtherism," and one uses it as his entire platform. There is a huge percentage of the population who still think that Obama wasn't born in the US, either due to racism or stupidity.
Let's face it, Republicans are idiots. In the 2000 primaries, there were rumors swirling that John McCain fathered a black baby (he adopted a Bangladeshi girl from an orphanage run by Mother Theresa). Others accused him of abandoning the veterans (while no one complained that Bush was never deployed to Vietnam.) You have to be stupid not to believe the Bush-Rove machine was behind these attacks. And you know what? People believed it. The same thing happened four years later, when a well-connected Texas group started to air ads that accused John Kerry (another Vietnam POW) of questioning whether he actually deserved his Purple Hearts and other awards. Bush and Trump, who are both from very rich families, avoided the draft. Clinton did the same, but had a Senator help him.