I'm glad it's been resolved and people learned something all around!
Couple issues here:
1. Changes to official paperwork, including all manner of legal forms, civilian and government, needs to proceed on a very clear basis which starts with WHY the information needs to be changed. The answer can't just be "because we don't like it". There has to be a real, legal justification for changing the information and it needs to be specifically called out. For example, "We have a notification in writing from the ATF that military institutions are not acceptable for birth place" or "Because AFB is not a commonly recognized abbreviation in the majority of civilian use, this must be spelled out as 'Air Force Base'". Or specific wording in the law which can be shown. Or an ATF audit finding in writing.
2. Once you sign a document, especially a legal, federal document like a Form 4473, you are saying, in legal terms, the information that was present on the document at the time you put your signature on it is correct. Altering the document afterwards means you're altering official paperwork. NOT GOOD.
These guidelines are good for ANY kind of paperwork you may put your name to. Changing anything after you've put your John Hancock on it isn't kosher, at the very least...and may be outright illegal as well. There are almost always some proper way of dealing with the errors. It may be as simple as a one-line through the error and initial/date next to the correction, it may be an official amendment form, it may be a complete reissue of the paperwork...whatever.
But do it right, whatever it may be.
I'm sure Frank Ettin can be far more specific about the shades of legalese involved, but in general I'm sure this will cover the issue in almost all cases.
Your gut instinct on this issue was spot on.