Child Ballad #79, Wife of Usher's Well - why birch bark?

On the sleeve notes of Peggy Seeger's album with the song on, Alan Lomax confidently says:

"in several versions of the song, the children return wearing (birch) bark caps, which is a sure sign of magic."

Can anyone give me clues why he is so confident about this?

Versions of the lyric:

"The carlin wife’s three sons came hame,
And their hats were o' the birk.
It neither grew in syke nor ditch,
Nor yet in ony sheugh;
But at the gates o Paradise,
That birk grew fair eneugh."
(Child)

"Her three kids come to her door
Their hats were made of bark.

And the tree never grew in any ditch
Nor down by any wall
But at the gates of Paradise
Grew strong grew tall."
(Martin Carthy)

From the ballad Scott Saunders (Chilx #69) the dead lover in the grave requests:

"But plait a wand o' bonnie birk,
"And lay it on my breast"

So is it associated with a funeral offering, like salt? Was there a Celtic association of it with rebirth? I guess birch sap can provide sustenance at a difficult time of year. It is a very fast growing tree, but I can't find a link to a specific deity or ritual or religious idea that seems relevant, or European mushroom that grows with them, to link them with magic.

I found one claim birch trees were planted in graveyards to keep the cattle off graves - that seems very weird to me, and I can't find any other backing for it.

There is a Scandinavian tradition of birch bark hats, associated with wild-living, and so maybe shamans?

Birch-tar was an ancient substance, maybe with symbolic links to sticking the spirits down? Or again, wild living and ancient woods knowledge?

Gillyflowers are meant to have sprouted from the tears of Mary and represent her virtues, and the carnation's name dianthus apparently indicates 'flower of Zeus', probably relating to their heavenly scent. There is a link to cloves, and incense. So I can see why 'set about with gillyflowers' evokes heaven. But why birch at the gates of Paradise?

Could it link to the tree the Golden Bough is taken from, in the Aeneid? It seems people expect that meant mistletoe, and it's role in part-poisoning into otherworldly journeys, as the druids were thought to have used it..

There is maybe a link to Lugh, who possibly is linked to Mercury, and do psychopomp..? His attributes in the Celtic world seem more to do with craft and warriorship than magic though