It has been suggested that the story reflects a time after the 1848 abandonment, when the ships had been remanned, discipline had broken down, and rival factions of the expedition's company were eking out a squalid, savage, existence and possibly resorting to cannibalism.
In contrast, I suggest it may reflect a far happier state of the expedition between the besetment of 12 September 1846 and Franklin's death on 11 June 1847.
With the vaguries of the old lady's memory, Tookoolitoo's interpretation, and Hall's notebooks, we can not be certain that every nuance of meaning in the transcribed version was intended by the original witness.
For example the sentence:
"Before the Captain took him down into his cabin he told this Innuit to take a look over to the land, the Captain pointing out to him the exact spot where there was a big Tupik (tent)" does not explicitly state that the Tupik was on the land, nor that the land was itself visible. Quite possibly the tent was in the direction of the land from the ship, but the land itself was many miles distant.
The first thought which ocurred to me was that the Tupik seen by the driver could have been canvas housing over the second ship. Another possibility is that it was a hospital tent, which would explain why the Captain didn't want the Innuit to go there.
Edward Belcher believed that the structure at Beechey Island identified as a washhouse was "more likely to have been an hospital". If the theory that the ships' water systems were a cause of lead poisoning is correct then a spell in such a hospital would likely be effective.
The weirdest part of the old lady's account is her graphic demonstration of the black men's "little black noses" - "not more than half the length & size of common ones".
Quite frightening although not inappropriate for the frigid regions. It's from the Wikipedia article "Balaclava (clothing)". I'd call it a ski-mask rather than a Balaclava, although there are really only a few stitches difference. Something similar was also apparently improvised by a member of Scott's 1910 Terra Nova Expedition.
There is, however, no evidence that anything resembling a balaclava was issued to the 1845 expedition.
The 1875 Nares Expedition seems to have been the first polar expedition to have been supplied with anything like balaclavas although at the time they were called "Helmet Caps", "Eugenie Helmets" or "Eugenie Wigs", as they were presented to the expedition by the exiled Empress Eugenie of France. The name Balaclava dates from the early 1880's.
Prior to the 1875 expedition the "Welsh wig" was the approved head garment. Similiar to the medieval "coif" - a close fitting cap that covers the top, back, and sides of the head.
"Welsh wigs" were among the list of clothing "served out to the men, on the first of July"  during John Ross's Victory Expedition. They were also included in the list of sledging equipment recommended by McClintock in 1851.
However in October 1843, Henry Powell of 102 New Bond St. registered a new design of night cap. Apparently identical to a Balaclava in form, it was widely advertised in 1844 as "Powell's Tempar Cap", so it is just possible that this garment was carried on the 1845 expedition, and is connected to the story.
Another possibility is that the men were masked with black crape cloth (crêpe de Chine). This had been recommended by Parry as a piece of equipment to avoid snow-blindness. (He also recommends a Lead-Acetate eyewash!)
It was also included in McClintock's list of recommendend equipment and it's effectiveness was praised on a searching expedition:
"As a preventive of this complaint a piece of black crape was given to each man to be worn as a kind of short veil attached to the hat which we found to be very serviceable."
At least a version of the fabric can be proven to have been taken on the 1845 expedition as among the relics brought back by McClintock are "a pair of leather goggles with crape instead of glass, a small green crape veil".
These are two possibilities which should be counted with other explanations.
My favoured explanation is that Franklin kept a happy ship and the black men were simply members of the ship's company indulging in high spirited horseplay. If this is the case then the unforseen consequence that contact with the inuit was curtailed may have been truly unfortunate.