In Kilayim 9:5, the Mishnah states that a merchant who sells clothing is allowed to pile on himself the shaatnez he is selling as long as he does not intend to benefit from it. The Gemara (Bava Kama 113b) explains that this Mishnah is in disagreement with the Mishnah cited in the question, about whether davar she'eino mitkaven--an unintended outcome--is prohibited or not. The Rambam, however, rules in accordance with both Mishnayot (Hil. Kilayim 10:16,18). Kesef Mishneh distinguishes between wearing--as in the case of the tax collector--which is forbidden, and merely putting on oneself, which is permitted. If so, without the Mishnah one may have thought this was permitted because it is davar she'eino mitkaven and we may not have distinguished between wearing and putting on oneself. It should be noted that while Shulchan Aruch follows the Rambam (YD 301:5), Rema (YD 301:6) rules against the Rambam and permits wearing the shaatnez to escape the illegal tax collector.