At least from two points, a layman such as myself, can negate it. That is, Ural Altai language is known to have "vowel harmony." Perhaps most vividly, in Finnish, the language still keep strict vowel harmony. On the other hand, there is no accepted theory that Ainu has the feature.
[Add:98/03/01; rev.98/08/25]
Also to be noted is that CHIRI stated the existence of vowel harmony may not give positive indication of a language belonging to a specific language group, say, Altai. He presented that several American languages and Bantu (African) language have vowel harmony. [end of addition]CHIRI Mashiho says there is vowel harmony in Ainu in his essay written in 1957.I am not aware whether his theory has been accepted. He showed many samples of vowel harmony existence. The existence, however, is between "word root" and "suffix." The suffix is in two groups, one making an intransitive verb a transitive one and the other personifying a word. Personifying, here, means for example, BOOK being basic form and MY BOOK being one of personified words. Finnish language's vowel harmony is "within word root" and "between root and suffix". Perhaps because many Ainu words are of mono syllable, his discussion was not very extensive in establishing vowel harmony "within a word root". Presently, I have a certain amount of reservation as to whether the phenomenon that CHIRI pointed is a vowel harmony or simply a convenience for pronunciation.
Another point is that in Ural Altai langauge, no words start with an "R". Ainu has a lot of words that start with an "R". About 5% of pages of a dictionary is under "R".
Kind readers have advised that there are words starting with an "R"in Finnish. However, we have agreed that they were all borrowed words. In the modern Japanese, another language suspected to relate to Altai, we have many R-starting words, all of which are borrowed words mostly Chinese vocabulary.
Shichiro Murayama proposes that Ainu and Austronesia languages are related from, what I see, his meticulous comparative language study methodologies.
Thank you again for your interest.