If a loved one flat-out refuses to go to a nursing home, and they truly have to be in one, is it OK to fib and tell them it's a temporary stay?

Absolutely - lie through your teeth and feel good about the INTENT behind it. You are not lieing to take their money or be manipulative, you're lieing with their best interests at heart. Often patients are referred to a nursing home for rehab or therapy but it doesn't go so well and they end up staying. At this point all you can do is be an advocate for their quality of life, their safety and their health care. Tell yourself their safety, nutrition and cleanliness come first and repeat it over and over.
Best of luck