How can you tell which noun a clause modifies?

I'm a ESOL teacher, and I'm having trouble answering a question that a student asked me recently. We were going over long sentences, and found this one from the New York Times:

Saudi Arabia said Tuesday that it was halting a nearly month-old bombing campaign against a rebel group in neighboring Yemen that has touched off a devastating humanitarian crisis and threatened to ignite a broader regional conflict.

It's clear to me, as a native speaker, that the clause "that has touched off a devastating humanitarian crisis and threatened to ignite a broader regional conflict" applies to the noun phrase "a nearly month-old bombing campaign" and not the noun phrase "a rebel group in neighboring Yemen," but I can't exactly explain why. I think I know this mostly from the context, but it wouldn't necessarily be obvious to someone learning English.

It would be possible to write this sentence with a clause modifying " a rebel group in neighboring Yemen." Something like, "Saudi Arabia said Tuesday that it was halting a nearly month-old bombing campaign against a rebel group in neighboring Yemen, which has been opposing Saudi influence for nearly three years."

Is it just the comma that makes it clear that one clause applies to the rebel groups, and the lack of comma that shows the clause applies to the bombing campaign?

Any help would be much appreciated! Thank you,

Lee

We need to look at the context of the article. If this sentence stands alone, which it does in this post, then we really have no way of knowing which noun phrase the clause "that has touched off a devastating humanitarian crisis and threatened to ignite a broader regional conflict" refers to. I would assume it refers to Saudi Arabia's bombing campaign, but it could just as well refer to the rebel group, and I wouldn't blame your students or anyone else, native English speaker or not, who assumes otherwise.

Reading the original article, it is clearer that the clause in question refers to the bombing campaign. The sentence "The bombing campaign, which has received logistical and intelligence support from the United States, has drawn intense criticism for causing civilian deaths and for appearing to be detached from a broad military strategy" implies that the bombing campaign is the thing causing "a devastating humanitarian crisis" and "ignit[ing] a broader regional conflict", not the rebel group.

Therefore, my answer: Don't take anything out of context. In the age of sound bites and snippets, anything and everything can and will be misconstrued, including the clause in question.