Closure gets confused about property types when not annotated

closure_properties.js

/** @interface */
function Gum() {}

Gum.prototype = {
  /** @return {boolean} */
  isMinty: function() { return true; }
};

/** @constructor */
function Candy() {}

Candy.prototype = {
  /** @return {string} */
  flavor: function() { return 'cherry'; }
};

/** @constructor */
function Thing() { }

Thing.prototype = {
  /** @param {Gum} gum */
  setGum: function(gum) {
    /** @private */
    this.gum_ = gum;  // Missing type in annotation. Closure seems to infer
                      // the type, but on closer expection it seems to treat
                      // it as a union of prototypes, somehow.
  },
  chew: function() {
    if (this.gum_.isMinty())  // Doesn't warn
      console.log('yummy');
    if (this.gum_.flavor() == 'cherry')  // Doesn't warn, but is a TypeError
      console.log('gross');
    if (this.gum_.nonExistentFn() == 'cherry')  // Does warn
      console.log('gross');
  }
};