I did some further research into the matter and determined the following (although of course, I am not a lawyer).
The short answer is that it's perfectly legal. Reverse engineering software (and the files it creates) is ruled as fair use in the United States, as established by Sega v. Accolade. The case, and other legal matters relating to reverse engineering software, are described in great detail in this article from the Yale Law Journal (the part about software is on page 1608). Even if the output document were to be classified as a trade secret, reverse engineering trade secrets is also legal.
Wikipedia lists a number of projects, that legally use reverse engineering, specifically mentioning OpenOffice.org and others reverse engineering the Microsoft Office file formats. (Heck, Wikibooks even has the book Reverse Engineering/File Formats that gives you advice on how to do it). At the end of the day, the legal precedent would be that you are covered, although of course each legal situation is unique.
As the Yale Law Journal article notes, not everybody is happy about reverse engineering software and some believe that it ought to be illegal. If the competitor sees it, they will probably be unhappy about the process since it might drive users from their product to yours and damage their sales. However, since that's the goal in the first place, that's probably not a concern.
It's possible that the company could see what you're doing as ethically wrong and give you all sorts of flak for converting their files. While we'd hope they would be professional about it, there's a small chance that you may have to deal with it. More likely though, they would implement the means for converting your documents if they thought you were a big enough concern. I wouldn't recommend converting their documents if you're not alright with them converting yours in return.
At the end of the day though, the choice is up to you and, like anything that involves other companies, there is an element of risk. While I believe that converting documents would be just fine and has a relatively low risk, each person will ultimately have to decide for themselves if they are alright with it.