The similarities among mother/mom (English), mádre (Spanish), ma (Chinese, sorry if the intonation is wrong), ma/mata (Hindi) has perplexed me.
The progression of sounds that a baby learns is well understood, especially the physiological aspects of language development and acquisition.
If we accept as a premise that cultures would tend to assign words most relevant to babies according to their physiological capability, then it becomes obvious why words for mother, father, and even facial features would be strongly similar across cultures. And why the similarity will slowly diminish as the meaning of words becomes less important, functionally, for communication with a child.
And especially for simple words the phonetics would have very little to do with cognitive development (and evolutionarily-dictated language models), but be controlled almost entirely by a baby's physical constraints--e.g. huge tongue in a tiny mouth, poor motor control, etc.
For everything else, not so much.
And especially considering that the researchers "reduced all sounds to 34 distinct consonants and 7 vowels." (Consider that the more we reduce and simplify the vocalizations the more likely we should expect correlations. For example, if we simplified all sounds to grunts we should expect tremendous overlap.)
The correlation of the corpus of 100 words isn't particularly surprising given what we already know about language development. The null hypothesis was that there'd be no correlation whatsoever (i.e. the sounds would be completely random), which I don't think anybody could reasonably expect.
There are also cognitive development constraints, of course.
The question is, from where do we get the correlation? If it's physiological or neurological, then there's nothing to support fanciful claims of innate language models. It's the cognitive constraints that can support fanciful claims, but you have to first show that it's those constraints, rather than the physiological or neurological constraints, that are controlling word choice.
Arabic: ami, ab
Chinese: ma, ba
Zulu: umama, ubaba
It's "obaasaan" in Japanese, though. It'd become "baa" if you remove the polite syllables, and thus also ends up becoming a labial consonant (ओष्ट्य for those familiar with the verse in पाणिनी).
Curious indeed.