"Lloyd generally represented his versions of "Reynardine""
I suggest you check on the Roud index to see how old Reynardine is, how far it has spread and how many times it has been found - it gives 146 references to the song.
It has also been given a Laws number (P15), which indicates that it was Current in the United States.
Laws' note to the song reads:

BRITISH BROADSIDE BALLADS TRADITIONAL IN AMERICA

P 15 RINORDINE
A man makes love to a girl he meets by chance in the mountains. When she asks his name, he cautions her against telling her parents, who would cause his death, and says that his name is Rinordine and that he has a castle in the forest. The ballad ends with a warning to maidens against walking at night and meeting Rinor.

One evening as I rambled two miles below Pomroy,
I met a farmer's daughter all on the mountains high,
I said, "My pretty fair maiden your beauty shines most clear,
And in these lofty mountains I'm glad to meet you here."

Thomas, Devil's Ditties, 108, 7d, m. (Ky.). Belden, 286, 12 (Kan.); equiv. of 10 (Mo.). Combs, 165, 8 (W. Va.). Chappell, 84, 13, m. (N.C.). Eddy, 192, 14 (O.). Gardner, 96, 19 lines, m. (Mich.). Flanders-Barry, 64, 6, m. (Vt. A different text with its literary source reprinted). Mackenzie, 102, 7d (N.S.) Detailed refs. Randolph I, 379, Id, m. (Ark. from ms.).
JFSS I, 271, 2d, m. (Sussex).
Broadsides: (B) Bebbington, 7d ("Mountains High". Harvard IX, 117). Such, 7d ("The Mountains High" Reprinted in JFSS I, 271). (A) N. Coverly, Jr., Boston (Thomas Coll. I, 55, "The Soldier and His Fair Maid". 6d and I, 64, "Ranordine", 7d). Songsters: (A) The American Songster, Phila., 1836, 191, 7d. The Forget Me Not Songster, Phila., 18, 7d. The same, N.Y., 199.

The fact that a song has been claimed from only one informant is immaterial - we have submitted a few dozen songs to be given Roud numbers which have only one informant, yet all have been obtained from a traditional source.
There is no reason to believe Bert didn't get The Recruited Collier where he said he got it - he was more prone to adapting songs, in my opinion.