You have the answer to your primary question.
The reason many rental markets are seeing increases is because of the "natural" demand brought about by Homeowner foreclosures.
These links might also prove useful for understanding "who can do what when".
And many cities have Housing Departments that govern tenant rights, so you may want to check to see if Chico has one for further guidance. Good luck.
And you have the right to decide you don't want to pay the higher rent and move.
All of that, of course, must occur within the terms of any lease. Thus, in the middle of your lease your landlord can't simply say: "Forget the lease. I'm raising the rent." But upon lease renewal, your landlord can propose to raise the rent. (If there are city rent controls, a proposed increase must be wthin allowable parameters.) And you can decide whether you wish to pay it, or whether you want the lease to expire and find a new place.
Incidentally, home valuation has nothing to do with rents. Rentals and sales are two parallel markets, not the same market. You often have situations where one is going up and the other is going down. And I can show you where $900 rents a $50,000 home and another place where $900 rents a $200,000 home.
Hope that helps.