The only way the doctor would get a $300 deduction is if they use accrual accounting and had already reported the $400 as taxable income. It's isn't a free deduction that comes out of nowhere.
With accrual, you report income when you bill for it, not when you receive it. Suppose you treat a patient on December 31 and bill the insurance $400 on same day. You report the $400 as income and pay taxes for the entire $400 in that year.
The next year, insurance only pays $100, so now you have a $300 loss to report in the new year. But you only have this loss because you've already reported the $300 as income.
If the doctor uses cash accounting, there would not be a $400 income entry on December. There wouldn't be any income to report until they are actually paid, and then the income is the actual amount they are paid, $100.
With accrual, you report income when you bill for it, not when you receive it. Suppose you treat a patient on December 31 and bill the insurance $400 on same day. You report the $400 as income and pay taxes for the entire $400 in that year.
The next year, insurance only pays $100, so now you have a $300 loss to report in the new year. But you only have this loss because you've already reported the $300 as income.
If the doctor uses cash accounting, there would not be a $400 income entry on December. There wouldn't be any income to report until they are actually paid, and then the income is the actual amount they are paid, $100.