You can only effectively take a deduction for the basis you have in the miles, which in a lot of cases is $0.

If you took $40,000 of flights to get the 70K of miles, and you previously deducted the full $40,000 of flight costs, your basis in the miles is $0.

If you bought $70,000 worth of business goods and deducted the $70,000, your basis in the 70K of miles is $0.

Most people do not assign any value to the miles they earn, so their basis in the miles is $0. In the Citi example, if a person did in fact report income from the receipt of the miles he would have basis equal to the amount reported as income, and if he could show that he used those specific miles for business without compensation, he should be able to take a business deduction for the use of those miles. This is very much the exception to the rule, though, since the Citi transaction was unusual.

If you take the position that the miles are deductible at FMV of $1,750, and your basis is $0, you have to recognize $1,750 of taxable income in order to take the deduction of $1,750, which does not produce any real benefit.

There are some posts in the 1099 thread that would disagree with some of what I just posted, including one from an attorney who does take some deductions for the use of miles (though not exactly in the manner that your post suggests, or in the amounts you suggest), so you might review that thread.