Assumption

The researchers' hypothesis is that "certain people survived the [Black Plague] epidemic because they carried a genetic mutation, known as Delta-32". They then supported this hypothesis by testing people who's ancestors survived the plague - they were found to have a high frequency of Delta-32. We need to find an assumption that this hypothesis or its evidence relies on. In other words, we need to find an answer choice where, if it were untrue, the researchers' hypothesis or its evidence would no longer be valid.

A. We don't care about any disease other than the plague. Whether or not they could get other diseases doesn't impact their ability to survive the plague. This answer is out of scope. Eliminate.
B. Like with A, we don't care about other bacteria. We know that Delta-32 impacts plague bacteria, which is all that matters to surviving the plague. Eliminate.
C. The plague occurred in the 16th century, so Delta-32 would have been around at the same time as the plague. If Delta-32 hadn't existed in its currently form until the 17th century, then this would matter, but it doesn't. Eliminate.
D. Again, we don't care about diseases caused by other bacteria. We just care about whether people with Delta-32 contracting the plague. Eliminate.
E. Let's consider what would happen if this were not true. What if the plague DID cause Delta-32? This would mean that its likely the reason that the descendants of plague survivors so frequently have Delta-32 is because their ancestors obtained Delta-32 due to the plague, survived due to chance/some other factor, and passed on the Delta-32 mutation to their descendants. This would indicate that the support for the researchers' hypothesis is invalid. So the researchers' hypothesis relies on this statement being true.