How come they don't singe after they are tanned? I assume people wear them in the sun. Is it the sun drying out wet fur that's the problem?

Because they are tanned,only raw otter fur singes.(Unless you hold the tanned pelt near fire)
Tanning furs is called dressing because the hair is treated (protected) with oils during the tanning also.

Or it is, at the very least, greatly exaggerated to separate the trapper from money which he is due.

I have also wondered this.

If you look at a unsinge otter or mink and one that is singe you will see a different in them.

Thanks Boco. I usually tan my own stuff but I'm tempted to send him off to the tannery

I would love to see a wide by side picture.

I have seen otter fur singe during home tanning.
A bit about singe on Otter.
A lot of otters caught late will have Naturally singed guard hair from their environment.Sun and heat cause it.It starts on the tail and works its way up the back as the spring season progresses.I have never caught a November otter that is singed.Otter guard hair is prone to singe because the hair is not round in cross section but oval,so the hairs all bend(curl) in the same direction when singe occurs.This makes it very noticeable.
I have sold my share of otter over many years at auctions and singed or pt singed otters at times bring as much money as strait hair grades.When otter are used for plucking and shearing there is little difference in price.When the market requires a natural skin,singed skins will bring noticeably less money because they can only be plucked and sheared.
when I started trapping otters years ago I ruined a couple by singing the fur in the truck cab,from the heat blowing on them.
I also seen a couple of otter pelts stored in an attic over the summer that were nice skins but were extremely badly singed when they were brought out.

I would too.

Where can I buy these magic oils so I can protect my otters from singe?

I have also caught and sold my fair share of otters and mostly agree with Boco's take on singe and its causes.

Sometimes you will catch an otter and have it expire up out of the water in direct exposure to sunlight. That will singe an otter in a matter of hours.

52 carl,Fur dressers generally protect their trade secrets.
Knoblochs used to sell a product called hair sheen,not sure if it is still available,regardless it wont help raw fur.Its effective only after the pelt has gone thru the preservation of the dressing process.