The government has land which they claim to be public land; if this is the case than one need not worry about what an individual landowner would do, since everybody owns government land. Therefore the government cannot prohibit hunting or fishing on government land.
If there was no such thing as government, and therefore no such thing as government land, then one could assume that things would be far more different than they currently are; and that there would possibly be no need for people to be on other people's property.
Property rights would be equal to all other rights. A starving individual has no more authority to prohibit you from using your property -while they hunt and fish- then you have to prohibit the starving individual his life. The starving individual would actually be violating the property owners rights by hunting or fishing without permission, and therefore would be in the wrong. This is the case, because the property is static -it doesn't move- and as such the starving individual could easily move somewhere else to do his/her hunting and fishing.