I've worked with some clever animals, and agree they didn't show any signs of recursive embedding (they "lex" but don't "parse"), but must note that modern anglophone humans are relatively embedding-impoverished compared with prior centuries, a reduction which we can observe in comparing the number of stack levels necessary to parse the subordinations and coordinations[1] in the dendritic periods of the 1st president of the US with the number necessary to parse the sequential utterances of the most recent.
[1] https://www.archives.gov/exhibits/american_originals/inaugtx...
> "In these honorable qualifications, I behold the surest pledges, that as on one side, no local prejudices, or attachments; no separate views, nor party animosities, will misdirect the comprehensive and equal eye which ought to watch over this great assemblage of communities and interests: so, on another, that the foundations of our National policy will be laid in the pure and immutable principles of private morality; and the pre-eminence of a free Government, be exemplified by all the attributes which can win the affections of its Citizens, and command the respect of the world."