Sentence Correction

In late 1997, the chambers inside the pyramid of the Pharaoh Menkaure at Giza were closed to visitors for cleaning and repair due to moisture exhaled by tourists, which raised its humidity to such levels so that salt from the stone was crystallizing and fungus was growing on the walls.

(A) due to moisture exhaled by tourists, which raised its humidity to such levels so that salt
from the stone was crystallizing

(B) due to moisture that tourists had exhaled, thereby raising its humidity to such levels that salt from the stone would crystallize

(C) because tourists were exhaling moisture, which had raised the humidity within them to levels such that salt from the stone would crystallize

(D) because of moisture that was exhaled by tourists raising the humidity within them to levels so high as to make the salt from the stone crystallize

(E) because moisture exhaled by tourists had raised the humidity within them to such levels that salt from the stone was
crystallizing

A, B are easy to eliminate here. The OG refutes option C, D stating that the pronoun "them" seems to refer to the tourists, which is quite the case. However, I do not clearly understand why the same criterion is not used to reject E.

Now while I understand that if we assume that the pronoun "them" in option E refers to tourists then it would make the sentence illogical and we would not have any right option here, however, can someone clearly explain how such options should be dealt...not just in this question but in any such question in general.

Many thanks

Siddus