In Cyril Edward Robinson's book "A History of Rome" he describes how freedmen could join the army in ancient Rome. Has this been corroborated anywhere? Are there specific examples?
This would probably have varied over time. Further, it depends largely on what you mean by army (just the legionaries? all combatants? everyone accompanying the legions?).
In the late Republic and the early Principate, the legions were exclusively composed of Roman citizens. Freedmen were not Roman citizens, but their children were.
The navy, on the other hand, was happy to enroll freedmen. Actually, under Claudius especially imperial freedmen for command functions, many others as rowers. At other times, even slaves were eligible; in the second Roman-Carthaginian war, for instance (after the Romans had managed to get three different Roman armies annihilated by Hannibal Barca), Sempronius Gracchus led two slave legions in the battle of Beneventum. Marcus Aurelius again accepted slaves into the army as stated in the Historia Augusta 20.6.
At any time, while freedmen could not ordinarily enrol as legionaries, there were plenty of freedmen (as well as slaves and others; as camp followers) in and around a roman army in the field (read about it here). Just to provide some intuition, Cassius Longinus ordered his freedman Pindarus to kill him during the 1st battle of Philippi, so it is safe to assume that he normally had Pindarus follow him around on the battlefield.
Also, have a look at "Valerie A. Maxfield (1981) The Military Decorations of the Roman Army, p. 129": There is not a lot of evidence that freedmen received military decorations. There are some exceptions like Numenius and Aurelius Nicomedes, but the evidence in those cases can also be called into question. The point remains that it is not that they were not employed as soldiers, but that they were typically not considered to have sufficient status and standing to receive honorable positions and decorations.