Stoic or Cynic?

I am busy these days revising my translation of the fragments of Musonius Rufus found in Stobaeus. This Musonius was either the Roman Stoic who flourished in the third quarter of the 1st century AD and was a teacher of Epictetus, or an Athenian Cynic and writer whose floruit probably belongs at the end of Hadrain's reign. 20th century scholarly consensus inclined to the former identification, but I lean strongly in the other direction. Here is a translation of his essay on training, an excellent point of comparison with Epictetus essay of the same name at Discourses III. 12.

Musonius' On Training

Employing arguments such as these, he [Musonius] was always vehement in encouraging those around him to engage in training. Virtue, he said, is not just a theoretical science, but also a practical one, like medicine and music. Just as a doctor or a musician must have absorbed the principles of his art, but also trained to perform according to these principles, so too the man intent on goodness must not only thoroughly understand the many precepts leading to virtue, but also train with these precepts in a way that shows a love of honor and hard work. Otherwise, how could someone straightaway become able to control his passions if he merely recognized that one must not yield to pleasures, but was actually untrained in resisting them? How could someone become just, having learned that one must love fairness, but having no training in rejecting avarice? How could one acquire courage, having learned that the things that seem terrifying to many people are not to be feared, but having never practiced being unafraid in the face of such things? How could one become prudent, having learned what things are truly good and what things evil, but having never practiced disdaining those things that merely seem good? Training, therefore, must follow learning the precepts appropriate to each virtue, if we are actually going to derive any benefit from this study.
To the extent that philosophy is a more important and more arduous pursuit than all the others, training becomes even more necessary for a person professing philosophy than for someone pursuing medicine or some similar art. Those who aim at these other arts [ start out with a big advantage], not having had their souls corrupted beforehand, nor having learned the opposite of what they are about to study. But those who attempt philosophy come to it already corrupted in many ways, and full of evils, and they pursue virtue in such a way that they naturally have need of more training in this.
How then, and in what way, should these people be trained? Since it hasn’t happened that man is soul alone, or body alone, but some kind of synthesis of both of them, the man who is in training must be concerned about both, but about the better part more, as is fitting, that part being the soul. But also about the other part, if he is not going to be deficient in any part of a man. For it is certainly necessary that his body be well conditioned for physical labour—by his body I mean the body of the philosopher—since often the virtues employ the body as a necessary tool for the business of living.
There is, then, one kind of training that pertains strictly to the soul alone, and another that is common to soul as well as body. Training in common, then, will pertain to both, as when we become inured to cold, heat, thirst, hunger, plain food, hard beds, avoiding pleasures, and patiently enduring toil. For through these things and things of this sort the body becomes strong, and inured to suffering, and tough, and fit for any work. The soul for its part is strengthened by being trained both in courage by the patient endurance of hard work and in self-control through the avoidance of pleasures.
Training peculiar to the soul consists first of all in preparing ourselves with proofs, both those that concern apparent goods, as not really being goods, and those concerned with apparent evils, as not really being evils; and in discussing the things that are truly good, and becoming accustomed to distinguish them from things that are not good. Then it goes on to practice not fleeing from any of the apparent evils, and not pursuing any of the apparent goods, and turning away from true evils by every means, and going after true goods in every way.
In summary, then, enough has been said about the nature of each kind of training. Nevertheless, I will try to expand on how each of them should be conducted, not by differentiating and distinguishing further between those exercises that are common to the soul and body and those peculiar to the soul, but by examining ( in no particular order) the components of each kind of training.
And so, although we have heard and understood these things, all of us who have taken part in philosophical discussions, that neither hard work nor death nor poverty is in any way an evil, nor any other things that have been freed from evil, and again that not wealth or life or pleasure, or any other thing not partaking of virtue is good, still, even though we have understood these things, because of the corruption implanted in us right from our childhood, and because of our bad habits arising from that corruption, we believe that when hard work is at hand an evil has befallen us, and we believe that when pleasure is present, we are in the presence of something good, and we shutter at death as the worst misfortune and cling to life as the greatest good, and when we give money away, we feel pain as though we were being injured, whilst when we receive it, we rejoice as if we were receiving something really beneficial.
To an almost equal degree in the case of most other things, we fail to deal with our circumstances in accord with the proper innate concepts, preferring to follow bad habits. So I say then that since all these things are the case, the man who is in training must try to make himself superior to pleasure instead of being well-satisfied with it. He must try not to turn away from hard work. He must try not to be in love with life nor afraid of death, and in the case of possessions, not put getting above giving.