I think that the confusion here lays with the use of External Chemicals. This topic normally comes up when talking about "Tail-pipe" fires,
Because the external chemicals are highly corrosive their use is not recommended WHEN POSSIBLE. Example: Engine Fire during start / shut down... "...Use bleed air / ground starter air to extinguish..." The remaining issue, is determining if it is a tailpipe fire, or a fire that can be combated with the on board equipment (within nacelle/cowlings, etc)
In-flight engine nacelle fires present different issues. Recently two 767 pilots operating for a Japanese based carrier blew both bottles when they experienced an engine fire during take-off. Both of them were presented with awards from their company for "Wrecking" that engine.
Which brings us to "Wrecking". I'm not sure I agree with this. Many years ago (about 16) a colleague operated an aircraft which was subsequently found to have had one of it's extinguishers discharged. The aircraft (Shorts Sky van) was operated like this for some time before the discarged bottle was was discovered (apparently an intentional coverup) I don't recall that the engine was damaged to any extent. Maybe one of the Engineers in this forum can speak more intelligently on this item.
Enter the issue of "Ambiguous Indications". The outcome of this scenario will be subject to the experience of the crew and other factors. An experienced group of folks may (or may not) see other factors (Bleed Air Leak, etc) and realize that a few seconds of thought before pushing that button or pulling that handle may yield a different end result. Additionally, an understanding of the type of fire detection system installed on the aircraft may prove beneficial.
Examples:
Photocell type detector which detects light - A slight change of heading or bank angle, and the fire disappears. Engine Fire? Without any other indication, I'd say ...probably not.
Heat Detector type - Pull thrust toward idle and fire warning quickly goes out. Move it forward again, slowly, and at some point the fire warning returns. Probably a bleed air issue, but again, will need to quickly review other indications.
There are several other examples which come to mind, and each would be handled according to their individual experience levels and circumstances.
That said, when it comes to safety, and more appropriately when it comes to an event that has compromised safety, the cost incurred with any successful solution (Extinguishing the fire) is irrelevant.
The bottom line; take a short moment to consider all the indications before deciding on the course of action, then do what's necessary to ensure a safe outcome.
On a similar, but separate subject. The chemical may (or may not) be corrosive, but they are definitely environmentally unfriendly. A few years ago some studies were conducted which looked at alternative types of extinguishing agents.
That study can be read here.
http://www.fire.tc.faa.gov/pdf/engine.pdf