The FCC doesn't make their decisions by popular vote. It doesn't matter how many people sign the petition. If the rules say the translator can be licensed, it will. This isn't like a reality TV show where people can vote someone on or off the island.
That's true. The rules regarding interference by secondary services (LP, TX, etc) still contain the words "ANY interference". This allows the primary station some very wide leeway, when defining the perceived harm a secondary might be doing to his station.
I've seen successful challenges to translators, based on as few as 2 or 3 complaints. A couple resulted in the translators being shut down, while others resulted in negotiated changes that eventually satisfied the primary operator.
If they're committed, I wouldn't discount KXXO's ability to pull this off just yet. The translator might get built, based on contours, but the real test will come when they turn it on.