If someone is going to punish me for what I find on MY property, fuck 'em.
A few bones or arrowheads or potshards aren't going to change the world, are not a Mayan temple (one thing is not like the other) and I refuse to suffer that academics may be entertained.
If I found bones, they'd be bone meal in my garden. If I found stone items, they'd be gravel, if I found pottery it would be dust, and if I found precious metals they'd be in a crucible meeting my cutting torch with some modern metals added to skew the assay.
If OTOH the government were to PAY for the COMPLETE costs of rescuing the objects and/or buy my property at a suitable profit, they could have at it.
What I buy and own is mine and I'd kill to protect it if I thought fit. Without property rights there is no (practical) freedom.