@pk - there has been a variance of opinion on this topic in many threads over the past few months.
There is one camp that shares your opinion that the interest is not deductible for the reasons you state.
There is another camp that states that because of 'tracing', the interest is deductible onto Schedule E, but certainly not deductible on Schedule A. Similarly, if the money was used to invest in a business, the interest would be deductible on Schedule C. But if the money was used to buy a vacation property, it would not be deductible because there is no 'tracing;' to Schedule A permitted, which is where interest on the vacation property would otherwise go.
