Clothes Without A Body

Rashi in Chukas (21:1) says יושב הנגב – זה עמלק, שנאמר: עמלק יושב בארץ הנגב (במדבר י״ג:כ״ט), ושינה לשונו לדבר לשון כנען כדי שיהו ישראל מתפללין לתת כנענים בידם והם אינם כנענים, ראו ישראל לבשיהם כלבושי עמלקיים, ולשונם לשון כנען, אמרו נתפלל סתם אם נתון תתן את העם הזה בידי.  If Amalek was trying to mess up the prayers of Klal Yisroel why didn't they change their garments as well so that Klal Yisroel would pray against the wrong nation?
The Or HaMeir on the Megillah says the following teaching from the Baal Shem Tov.

                                                           What I believe he is trying to say is that the evil forces don't have any true self; they only exist as a cover up, as garments over the truth.  It is impossible for Amalek to change their garments for that is their entire existence.  Amalek without its clothes ceases to be Amalek.  Amalek was trying to disguise itself as כנען but not steal their identity.  In order to maintain their own identity, Amalek must remain in its own garb.