BORAS ?
A city in Sweden (thank you, Mr. S!!!)
If the score is 1 or above then R is the third letter, because the only switch from BORES was E->A, ad since the letter in common between PURER and BORES were E and R and they were both 1, meaning it was one of the two, and only E was changed, butthe score stayed the same, meaning that R had to be the third letter.
If the score is 0 then E is the fourth letter because the only change from BORES was E->A, and since the only letters in common from PURER and BORES were R and E, and they were both 1, meaning it was one if the two. Since E was changed, the fourth must be E.