Anyone lose their cards to/from an auction house?

[Tsaiko]

I hinted at this question in the "Anyone lose a package through PSA?" thread, but didn't get a response, so I want to try again.
I'll assume, based on the info from the other thread, that PSA is not a large enough organization to carry their own insurance, but apparently auction houses, at least some, are.

These are the shipping instructions from one auction house and I've heard these instructions from two others, so I'll assume it's pretty standard.

"Send Fed Ex priority overnight with signature required. Do not put a value on the Fed Ex slip. Fed Ex does not insure collectibles. This package will be insured by our Collectibles Insurance Auction House Policy underwritten by "xxxxxxxxxxxxx"." And they go on to give their FedEx number.

The above quote was in reference to a shipment for over 700 cards, valued over 6 figures.

So has anyone had to deal with a lost package to or from an auction house?

If so, what type of proof was needed and how long did it take to settle a claim? All I can do is scan everything I pack, but someone could have scans and only send newspaper. On the other hand, what happens if an auction house sends you cards, using their insurance, and the FedEx truck gets in an accident and burns?

These scenarios seem to be fraught with the same uncertainties that were brought up in the PSA thread, so I'm still wondering what's the safest way to ship cards, especially large amounts to grading companies and auction houses. From my research, registered mail seems to be the safest, but again, what about success in filing a claim? Sending 100k worth of cards via Registered Mail would take 4 packages each insured for 25k at a cost of about $50 per package, which would be well worth it if I knew I would be reimbursed if something happened to the package.