Cash out refi from primary residence - tax deduction?

[Corey M.]

If I take equity out of my primary residence by doing a cash out refi, and that equity is used to buy a rental property, is the mortgage interest deductible? Everything I've looked at seems to point to it only being a deduction if it's used to make capital improvements on your primary residence. But that doesn't make sense since you can do a cash out refi on a rental property and deduct all mortgage interest. A loan is a loan, so I'm not clear on the tax rules.

If the answer is no, that you can't deduct mortgage interest from a primary home cash out refi, why would anyone ever do it? Seems like it'd make more sense to just get a new loan on the property that can be fully deducted. This is significant. On a $200k house at 4% interest, you'd be missing out on an 8k deduction, which would likely outweigh the cost of the higher interest rate associated with a rental property. 

Am I wrong here?