In most places I'm familiar with...
Owning, renting, or leasing a property gives you basically identical rights from a legal perspective. Doesn't matter if you've owned the property for 50 years or you are renting a hotel room over night -- it is yours and you can do anything you would be legally allowed to do in any other property you possess. If it's a residence you have the same legal rights regardless.
In fact... in some states those legal rights extend to anything you use as a residence however temporarily. In California, for example, you are legally allowed to have a gun in your tent when you are camping because that tent is your home. You can concealed carry a loaded .45 inside that tent and nobody can stop you even if you are in the middle of an "gun free" state park. You may not be able to legally get the gun to the tent, and if they find out you had it they may wait until you leave and arrest you then, but while your tent is "home" they can't arrest you for having a loaded gun because in California you can have guns in your home.
All types of possession give you basically identical rights, including the right you grant those rights to others. Many leases, for example, specifically grant the landlord permission to enter in specific conditions. That may include stipulations that you not change the locks, or not add alarm systems, or whatever. That's a negotiated part of the price between you and the landlord. If the lease doesn't include permission the landlord can't enter.
Not all leases grant those permissions by the way. I was once renting office space and got a call from the landlord... they wanted to come over and do some maintenance for another suite by going through mine. What they wanted to do was legitimate and it wouldn't have been a major problem but I refused because it would've been a disruption. Their response was, "OK, it's your property and we can't come in without your permission." Of course there, when I took possession of the property, the first thing I did was call a locksmith out to rekey the locks. Same can be true with rented residences. My family used to rent houses and first thing we did when we moved in was change the locks.