My summer town extra player got the tarantula task. It wasn't a week long challenge. It was one day for 2 coupons.
Not rigged but not fair. It could be raining and impossible to catch.
It sucks sometimes (esp. for those who don't have a New!3DS + Amiibo Cards or the reader), but... oh wells. Nintendo isn't maliciously picking out the worst initiatives for a player on a given day. It's RNG just like the maps, villagers, fruit, grass, etc. Nintendo can't control the RNG of your particular copy and there's ways to get around initiatives if you can't do them or aren't willing to part with a few thousand bells for a day.
Nothing is "rigged." Sometimes we just don't have good luck with RNG.