The gemara suggests that even though one who damages pays from his best quality fields, m'doraysa, the mishna refers to it as "tikun ha'olam" because the tana of the mishna holds that we darshen the reason for the torah which is a tikun ha'olam to deter people from stealing. It seems very strange that the braisa asks why does a damager have to pay from the best of his own fields, and answers that it is to prevent robbers and thieves. What does robbers and thieves have to do with one who accidentally damaged another? The rashash suggest based on R' chiya in baba kama who lists a thief among the 24 avos nezikin, it would make sense. Presumably the rashash means to say that since a thief should pay from his best fields as a deterrent, so too all damagers must pay from their best so that we don't distinguish between one type of damager and another. I would like to suggest a different approach. This gemara is perhaps the source for Rabbeinu Yona (beginning of avos) who says that there is a prohibition to damage someone else's property since it qualifies as stealing. Basically people who damage are generally neglectful to some degree and therefore in violation of stealing someone's property. The braisa means to say that a damager must pay from his best fields to prevent "thieves", meaning those who are careless about damaging others and thereby in violation of stealing. By forcing them to compensate with their best fields, it will deter them from stealing.
M'inyan l'inyan, Tosafos (as explained by maharam) says that the issue of darshening the reason behind pesukim is only a machlokes when it makes a practical difference (such as here, by darshening the reason, the mazik will have to pay from his best rather than having to pay from the nizak's best). Meaning, all agree that we darshen the reasons of pesukim for the sake of learning and better understanding, but R' Shimon is of the opinion that even where it makes a practical difference in the halacha we darshen the reason to limit or expand the halacha. Tosafos seems to hold that R' Yehuda who does not darshen the reason of the pasuk, will maintain that we do not darshen the reason behind the pesukim anytime it makes a nafka minah, even if the nafka mina would be l'chumra. In other words, R' Yehuda only studies reasons behind pesukim as an academic pursuit, but rejects the entire notion of darshening the reason behind pesukim whenever it makes a difference l'halacha, even if it will result in a pure chumra (rather than just rejecting it when it results in a leniency) because he is philosophically opposed to the concept of controlling the Torah by human logic.
However, the Chasam Sofer (Teshuvos Y.D. 254) suggests that only for a kula (or monetary issues where a chumra for one is always a kula for the other) would R' Yehuda reject the notion of darshening the reason. But when it will result in a pure chumra, R' Yehuda would agree with the notion that the halacha of a pasuk would be controlled by the reason, and we would have to be choshesh for any reasons that would result in stringency that perhaps that is the "real" reason for the pasuk.