I went through this exact same thing at a previous job, and they also reacted like I was speaking another language. These weren't dumb people either, but they were very much the types who had never spared a thought to anything about technology, much less privacy.

They eventually offered to pay me a monthly stipend and put it back on me to use that to buy a work phone or just pocket the $. I didn't feel like going through that hassle, so I caved and just kept the money.