Have you looked directly at the Indiana State park's website, which no-doubt lists their rules ? Eg.: Dogs on leash, no fireworks, etc... And if so, if it's silent on the issue, then presto : Not disallowed.
And if you say that you DID go to the "park's website", and it says that you "need permission from the kiosk of the park-in-question", then I have a STRONG suspicion of how such minutia/wording made it into that link. Care to take a guess ? It's easy : Sincere md'rs, 10 and 20 yrs. ago, called and showed up at various kiosks asking "Can I ?". So the "pressing question" eventually makes it's way onto an FAQ type thing.
And go figure : Some parks in the state might have sensitive historical themes. While others are innocuous beaches, sandboxes, etc.... So what's the "safe answer" ? To: "Inquire at each one you come to". Which has what effect ? Simple : Legions more md'rs showing up at kiosks asking "Can I ?" And before long, the "pressing question" lands on the Indiana State park's staff archie's desk. And then PRESTO : A new law is born. A giant case of "no one cared till you asked", that takes decades to evolve. I've seen this happen first-hand
Because put yourself in the shoes of the rank-&-file kiosk worker who gets this question (that perhaps he's never thought of before, nor would he care one iota) : He's got to give an answer, so he picks up his phone and calls his superiors in state capitol. And the ball starts rolling from there.
As far as the "ask each property manager" answer: I have no doubt that, yes, each ranger DOES INDEED have jurisdiction over his particular park. And yes he DOES INDEED have ability to tell you "no" or "scram" (because he thinks you might harm earthworms). But why oh why oh why swat hornet's nests, and put it on his plate as a "pressing decision" before-you-even-start ? For heaven's sakes, if it wasn't forbidden in the first place, then why does this need someone's "princely blessing" before you can do it ? I mean, heck, no one asks "Can I fly frisbees ?", right ? So since when is md'ing so evil that it needs an express "yes" ?
Oh I know : It's when 100 of us have shown up asking, so they pass out the easy answer. Which makes its way onto an FAQ, then disseminated throughout the internet, blah blah blah.
It's as if we md'rs can be our own worst enemy !
Example: The "turn over everything you find" nonsense: Well gee, that can be traced to the fact that every park has prohibitions on "harvest and collect", right ? So that no one thinks he can take home the park benches, or start cutting down trees for lumber. Right ? So when the "pressing question" lands on their plate, some genius is sure to think "hmmm, this involves "taking things " (coins, pulltabs, etc...), therefore it falls under this rule. Oh gee, aren't ya glad you asked ?