In point of fact, Rand's assertion is almost certainly false. In any case, if it is a conjecture, it's been falsified by the "Iowa Gambling Task," an experiment that demonstrated the ability of the unconscious mind to make inferences on its own:
Participants are presented with 4 virtual decks of cards on a computer screen. They are told that each time they choose a card they will win some game money. Every so often, however, choosing a card causes them to lose some money. The goal of the game is to win as much money as possible. Every card drawn will earn the participant a reward. Occasionally, a card will also have a penalty. Thus, some decks are "bad decks", and other decks are "good decks", because some will lead to losses over the long run, and others will lead to gains. The decks differ from each other in the number of trials over which the losses are distributed.
Most healthy participants sample cards from each deck, and after about 40 or 50 selections are fairly good at sticking to the good decks.... Concurrent measurement of galvanic skin response shows that healthy participants show a "stress" reaction to hovering over the bad decks after only 10 trials, long before conscious sensation that the decks are bad.
In other words, the unconscious mind figures out which decks are bad before this awareness reaches the conscious mind. These findings are consistent with a large body of experimental research (see Timothy Wilson's Strangers to Ourselves).
“If your subconscious is programmed by chance, its output will have a corresponding character.” The phrase "programmed by chance" means something along the lines of: not sufficiently focused. Remember that according to Objectivism, the ultimate choice is to focus or not. Stated in its bald form, this seems extreme. Since any conscious person is, ipso facto, focused, this doctrine has to be restated in terms of degrees. It is the degree of focus that is important. One needs an intense enough degree of focus to be aware of one's own conceptual integrations, or else one will be prone to integrating errors. Those errors, once planted into one's subconscious, will lead to irrational emotions and other disturbing psychological phenomena (such as, par example, a fondness for "malevolent" art or music).
Did Rand provide any evidence for this view? Nope. Nor did she explain why she believed it. Then what reason can any rational person have for believing it? None whatever.
As anyone who has bothered to read some of the popular expositions about the "adaptive" unconscious knows, the subconscious (or unconscious--these words mean the same thing) doesn't work this way. The conscious not only processes knowledge, but makes decisions and organizes memory. The relevant evidence (see the above mentioned Strangers to Ourselves) strongly suggests that the conscious mind neither is nor could be in control all the time. The conscious mind, far from being a gate keeper of what goes into the unconscious, can at best merely provide critical testing of what comes out.
A “ruthlessly honest commitment to introspection” yielding a “conceptual identification of your inner states” allows one to discover the sources of one’s emotions. Same problem as before: how does Rand know this? what is her evidence?
Since it's now generally believed that the conscious mind is merely the "tip of the iceberg," Rand's advice about "ruthlessly honest" introspection seems misplaced. Since most of one's "inner states" lie below the threshold of consciousness, they cannot be introspected. It matters little how ruthless honest the individual hopes to be when the impossible is his goal. The attempt to introspect what cannot be introspected will most likely lead to little else but self-aggrandizing rationalizations.