You're right. If the IRS sends you a letter saying you owe something, the simplest thing to do is to send them a check. Normally, that is the end of it.
However, if the amount is substantial (substantial being variable for different people), some research should be done. An example is if your spouse, for example (no names mentioned) forgot to put a social security number and form number on the check she sent with the previous forms. Then, if you truly do not owe any money, it is worthwhile to obtain a copy of the cancelled check, as cashed by the US Treasury, and write a simple, clear letter explaining the omission. Eventually, that will clear things up, but it can take some considerable time.
Fortunately, the IRS, despite its dire warnings, does not act quickly, ever, except in cashing checks you send it. In one case, where that social security number was left off the check in question, it took three years and a number of letters, each with a copy of the cancelled check, before the IRS stopped demanding the money.
It was much faster this time, actually, to pay the amount twice and let the computer find the double payment and issue a refund. The amount, however, was only in the low three digits, so it wasn't that substantial.
On the other hand, one time I received an income tax refund from the State of California for more than my actual taxes amounted to. After looking at the calculations the state included with the refund, it was clear that someone had mistyped a number from the tax return when entering the return into the computer. I could see exactly what the error was.
I called the number listed in the mailing and attempted to explain what had happened to the nice person who took my call. He seemed not to understand what I was talking about, and did not offer any useful suggestions for what I should do with the overpayment in the check. The state actually owed me nothing at all.
I weighed what to do for some time. Now, I could have used the roughly $2500 that check wanted to pay me, but did not deserve it. I reasoned that someday, when i did not have $2500, the state would recognize its error and demand the money back. However, the human being I talked to offered no solution, and I knew, from experience that sending the check back with an explanation would probably just lead to additional hassle. So, I stuck the check to the wall of my office with a push pin and just let it hang there.
I never got a request for its return. I never deposited it. I finally threw it away 10 years later. Trying to correct an error with a government agency is almost always a waste of time.
And then there was the time when the sales tax department audited me in a visit from a tax auditor. How that ended is a story worth telling, but I'll save it for another day.
= new reply since forum marked as read