Why is Swift nil-coalescing returning an Optional?

First, I try mapping a [String?], to get a [String]:

$ xcrun swift
Welcome to Apple Swift version 2.2 (swiftlang-703.0.18.8 clang-703.0.30). Type :help for assistance.
  1> import Foundation
  2> let j: [String?] = ["a", nil]
j: [String?] = 2 values {
  [0] = "a"
  [1] = nil
}
  3> j.map {$0 ?? ""}
$R0: [String] = 2 values {
  [0] = "a"
  [1] = ""
}

This makes perfect sense to me. I nil-coalesce a String?, and I get a String. But with [AnyObject?], something strange occurs:

  4> let k: [AnyObject?] = ["a", nil]
k: [AnyObject?] = 2 values {
  [0] = "a"
  [1] = nil
}
  5> k.map {$0 ?? ""}
$R1: [AnyObject?] = 2 values {
  [0] = "a"
  [1] = (instance_type = 0x00007fff7bc2c140 @"")
}

I'm nil-coalescing optionals, but this time I get out an optional. Why?

The Swift Programming Language says a ?? b is shorthand for a != nil ? a! : b, but when I try that, I get out an array of non-optionals:

  6> k.map {$0 != nil ? $0! : ""}
$R2: [AnyObject] = 2 values {
  [0] = "a"
  [1] = ""
}

Am I misunderstanding how ?? is supposed to work? What is going on here?