No, I don't think they lifted their song versions from one another (necessarily). Most have unique/original versions which, with some caveats (depending on the source) are just as authentic/pure as any other. My comments were on the ideas they write about the songs. To some extent, these ideas affect their "version," but again that's complicated and can only be illustrated on a case by case basis.
Smith got this song from Alden's article. 1882 Alden, W.L. 1882. "Sailors' Songs." Harper's New Monthly Magazine (July 1882): 281-6.
She just reproduced the whole song (untitled) of "Hilo, my Ranzo." In fact, her collection contains every song that Alden published. The majority of songs in her text come directly from elsewhere, though there are also a signiicant number of songs that she did collect herself, including gems like "South Australia."
Colcord, of course, did do fieldwork for most of her songs. My understanding is that she would have only taken song material from elsewhere for certain cases where she did not come across the material in fieldwork, but wanted to be inclusive. So she includes some chanties, for example, from Robinson, like "John Cherokee."
1917 Robinson, Captain John. "Songs of the Chanty-Man: I-IV." The Bellman 23(574) (14 July-Aug 1917).
Colcord explicitly acknowledged Robinson. However, in the case of "Hilo, my Ranzo" (or whatever she called it), as per my comments above, I think she heard the song, perhaps the first verse only, and "innocently" fleshed out the rest using Whall's text. (Incidentally, Robinson also gave a one-verse version of this song, but Colcord did not use it -- she didn't need to.) It really seems unlikely that they would have the same exact words and punctuation if she had not.
Harlow learned most of the songs first hand, but he omitted or bowdlerized a lot when it came to publishing. There is also the issue that his voyage was in the 1870s but his final version of text didn't come out until 1962. His versions seem pretty credibly what you'd get in 1870s, but here and there I think he made up new lyrics for the solos -- since "one lyric is as good as the next." Also, from a 1909 article by a Buryeson, introduced to Mudcat by shipcmo and Lighter, we've seen that Harlow reproduced a few of those songs or padded a few of his songs with verses from them. It's my personal belief that Harlow may have used a couple other articles in that way. Lastly, the final section of the 1962 edition of Harlow's book is an assortment of songs that are culled from other texts. All those things being said, his version of "Hilo me Ranzo" looks to be totally independent.
Doerflinger collected all his songs or noted explicitly where he got them. He is the most rigorous of all the editors.
Hugill used a combination of techniques. If a song he gave was rare, then most/all or the verses are probably what he collected. But if the song had been printed several places elsewhere, he tended to combine verses from all of those , as if to give a sense of what the possibilities were. Sometimes the verses are authentic, sometimes they come from contrived settings by people like Davis or Masefield. If he knew the song from the oral tradition, usually he gave his own setting of tune and chorus; the borrowings mainly affected the solo verses. Hugill never explicitly says which verses came from where, or which ones he made up (albeit in true sailor spirit) at the time of publication. This vagueness helps maintain the image of his omniscience! However, he typically did mention, in the surrounding text, most of the editors whom he'd read.
In the case of "Hilo me Ranzo," I believe he said it was "my version" -- leaving us to assume he learned and perhaps sang this particular tune and chorus. The solo verses are from Whall/Colcord, Davis & Tozer, and other books and probably his own experience. The tune, as written, seems a bit awkward at times, and I have a suspicion that there may be errors in notation (pretty common in SfSS). I have a terrible rendition of it on YouTube that I don't want to revisit. :) Perhaps it's time to rerecord!