The following statement comes from a well-known sports medicine book that has gone through five printings. "In spite of the widespread use of NSAIDs there is no convincing evidence as to
their effectiveness in the treatment of acute soft tissue injuries." (Bruckner, P. Clinical Sports Medicine. New York City, NY: McGraw-Hill Book Company, 1995, pp. 105-109.)
This is a true statement, but definitely not strong enough. More appropriate would be something like, --In spite of the widespread use of NSAIDs there is substantial evidence that they hamper soft tissue healing.--
In the past, I have used NSAIDs in my marathon training quite regularly. I don't have anecdotal evidence that they hampered healing. My specific problem with taking NSAIDs (generally Ibuprofen) was that I would tend to not be conscious of pain from injury and run through it, causing additional damage which would take longer to heal, which would require additional NSAIDs to relieve the pain from.
In this last build-up of 1400 miles, I have probably taken 2800 mg of Ibuprofen for joint or muscle pain the entire time. Whenever I have, I have made sure to not run during its dose-duration of 4-8 hours, which usually means that I take it before bed or on a rest day. While this strategy doesn't resolve the slow healing problem, it at least ensures that I do not compound the injury.
Some more discussions of NSAIDs: