"usually by one's own exertions" does not fit contracting a disease or being infected.
In professional settings, terms get chosen for ability to reliably convey specific scenarios. I suspect that ability better determines their adoption, rather than how they might align with language norms of a particular decade.
The important bit in your wording above isn't the 'by ones own exertions' but: "to get as one's own"
Since these are people who caught malaria in the USA, rather than elsewhere and simply travelled here, the wording makes good sense.
One does not "acquire cancer" or "acquire STDs". Why would one "aquire Malaria"?
You usually aquire cars and houses and companies and a taste for coffee and good things - not Malaria.
Yes, you can also acquire a car, but I'm not sure why that might lead one to think that "acquired malaria" is incorrect...
AIDS stands for “acquired immunodeficiency syndrome”.
The poignant example being "acquire", which historically implied "getting by one's own efforts" but has drifted to be used more passively now.
So I guess diseases are similar? :-)
(I just checked and no immediate hits for "malaria virus sample" on eBay so probably not, hope I don't get a visit from the good people at Border Force for this. :P )
Be on the lookout for malaria appraisals on coming episodes of the Antiques Roadshow!
edit: wow, jokes are not well-received I guess