This is a bogus claim, because the alternative is simply not having the money. There are plenty of checking accounts with nonzero interest.

An example to make things clearer:

Imagine that you write 12 checks per year (one a month), each of which is in the sum of $1000. In case A they get cashed immediately in case B they get cashed one year later.

Case A: You make zero interest, each month $1000 is deducted from your checking account.
Case B: For the month you make $1000 * 1/12 of a year's interest. The second month $2000 * 1/12 of a year's interest. And so on until the 12th month where you make $12000 * 1/12 of a year's interest. Then things begin declining as the money begins getting taken out. (so month 13 is $11000 * 1/12, and so on). After 24 months, your $12000 has been deducted. However, assuming an interest rate of .6% (for ease of math), we would have made $720 in interest.

and

These two sentiments are why I'd trust your doctor. Everyone makes mistakes. Your doctor seems to be good at realizing when he did it, correcting his mistake quickly, and remembering it for a while (enough that he feels obviously guilty). That'd make me trust more that he'd care and do the right thing by me to the best of his ability.