:The source Campbell cites is the article on the Algonquin from the Handbook of North American Indians, but the source that article cites (which luckily I have!) is Gordon Day's 1972 article from the International Journal of American Linguistics, "The Name Algonquin" (IJAL 38(4):226-228). Apparently etymology deriving the name from a putative Mikmaq term algoom(e)aking ("at the place of spearing fish and eels") etymology comes from J. N. B. Hewitt in the Handbook of American Indians (NB: not the same as the Handbook of North American Indians, which is late 1970s-present; the first vol. of the Handbook of American Indianswhere this etymology appearedis from like 1905). Day refers to Hewitt as "the Bureau [of American Ethnology]'s Iroquoianist", and says of the proposed etymology: "Hewitt's form appears to end in a locative [i.e., -ing], thus agreeing with his translation, but a locative is not appropriate after a verb root, and if -ing is a locative, it is not a Micmac type locative. It is not clear where the -k- comes from. It may be observed, moreover, that although a people may derive its name from the name of a place, a place-name is not the name of a people." He goes on to mention a number of other possible etymologiessome apparently his own guesses as to potential sources from each of the languages spoken by Indians Champlain was with when he first recorded the name, rather than theories which had previously appeared in the literature. Champlain first recorded the name at Tadoussac in 1603, so if that's where he first heard the word, Day says, it would have come from the Algonquins, Montagnais, or an "Etchemin" (unfortunately, the French applied the name "Etchemin" to a bunch of different Algonquian-speaking groups, though Day here identifies them mainly with the Maliseet and Abenaki). Because Algonquin and Montagnais lacked the phoneme /l/ at the time, but Maliseet did have it, Day guesses the word came from Maliseet and suggests the word quoted in the WP article as the "most probable origin of the name" (but he never claims he's proven anything). 
 :Personally, I'm not particularly convinced by his evidence, but obviously that's unimportant for Wikipedian purposes; in any event his suggestion seems to be the one most frequently cited in recent literature. Besides Campbell and the HNAI, there's Bill Bright's Native American Placenames of the United States (which the Online Etymology Dictionary cites alongside the algoomeaking theory). The Random House Dictionary (and thus dictionary.com), whose Algonquian-related etymologies were written by Ives Goddard, simply says "presumably < an Algonquian language". At least some other dictionaries just mention the algoomeaking theory as the OED does; from personal experience I'll warn that dictionaries in general, but the OED in particular, tend to be quite bad when it comes to Indian etymologies. But of course that's irrelevant for Wikipedia's purposes. You're probably right that the alternate theory should be mentioned in the article, given its prominence in respectable and widely-consulted dictionaries