The behavior section sounds ambiguous to me.
http://docs.mongodb.org/manual/reference/operator/query/geoIntersects/
http://docs.mongodb.org/manual/reference/operator/query/geoWithin/

Behavior
Any geometry specified with GeoJSON to $geoIntersects queries must fit within a single hemisphere. MongoDB interprets geometries larger than half of the sphere as queries for the smaller of the complementary geometries.

A geometry in query doesn't have to fit within a single hemisphere. For exmaple, let's imagine we have a band around the equator as following. Visualize it by dragging the GeoJSON definition to http://map.visualzhou.com, or see the screenshot attached. It's impossible to cover this band with any hemisphere cap, no matter North/South hemisphere or any hemisphere. However, since its area is less than half of the surface area of the earth, MongoDB/S2 still interpret it as the band we want. So the area matters, rather than the span.

var band = {
  "type" : "Polygon",
  "coordinates" : [
    [
      [-170, 10 ],
      [-85, 10 ],
      [0, 10 ],
      [85, 10 ],
      [170, 10 ],
      [170, -10 ],
      [85, -10 ],
      [0, -10 ],
      [-85, -10 ],
      [-170, -10 ],
      [-170, 10 ]
    ]
  ]
}

var coll = db.geo_hemisphere;
coll.drop();
assert.writeOK(coll.insert({loc: [0, 0]}));
assert.commandWorked(coll.ensureIndex({loc: "2dsphere"}));

assert.eq(1, coll.find({loc: { $geoWithin: {$geometry: band}}}).count());