Ancient cultures with primitive cosmology could only anthropomorphise spiritual metaphors into corporeal-based realities due to early man's miscomprehension of abstract concepts. From my personal studies of Vedic scripture, I cannot say it is evident that the teachings mean that we cyclically return to a physical existence, as this would negate justice, mercy, or logic in the way the universe operates, but it definitely describes our continual progress in worlds to come. Reincarnation in the most abstract sense is mind-to-mind (moment-to-moment) psychological Coming and Going (Rebirth). Note that to be in "constant evolution" there can by law be no retrogression.
Only when we apply our mental faculties to higher realities do we perceive literalism contained in Vedic scripture. With spiritual eyes we can understand the allegories and similes expressing intangible, incomprehensible concepts. For example, the early Hindu-Buddhist philosophers and sages believed that class, health, and even infant mortality, were due to negative karma individuals perpetrated in past lives none of us can say we recall. Yet with modern science we have discovered the underlying causes in economic and biological sciences, as well as the means to control and eradicate many of these agents that are the causal factors behind these sufferings, revealing the superstition of our ancestors.
So, yes, there is doubt as to whether the Vedas state that souls reincarnate in the physical realm, when some Hindu schools of thought to this day have differing opinions on the matter. It is undoubtedly clear that souls journey from one state of consciousness to another and that the nature of the soul of man is eternal and continually evolving towards higher degrees of perfection. Consider how a dog, cow, an ant, or any other animal, is devoid of creative or rational thought which modern science has proven distinguishes our species--wherefore is the necessity or rationale behind being culpable for punishment or reward when this is dependent upon recollection of our "former consciousness" (Upanishads)? No animal has insight into past lives, let alone rationality, and if the argument is that we cannot talk to animals (which is not entirely true at all), then the argument is it is still "humanly" possible to be cognizant of past lives--so why can I not, nor the vast majority of any human being, do this so as to be genuinely responsible for punishment as a lower creature or rewarded as an endowed human being or god?
This is the sort of reasoning reincarnation theory runs into. My belief is that it is a theory devised by peoples who lacked science of biology to account for disease, race, differences in ability, birth, etc., therefore a neatly packaged philosophical construct of corporeal-related ideas is the only solution for our ancestors to cope and understand divine revelation. Keep in mind that the Divine Manifestations (Avataras) speak in the "creative word", so to assume they're using concrete concepts, when the Buddha is well-known (as Jesus) for using parable or metaphorical similes, is fallacious.
