Help! Spakers damaged during shipping?Paid insurance (with proof)being told not Insured?

Some here say that if you sign for the package then you are accepting it as-is. But seldom have I had to sign for anything, not even the Martin Logan speakers I bought last year — was told to expect the packages on a date and then when I checked they were sitting in front of my garage.  All other packages were just left by my front door.

Only once was a product delivered damaged.  It was a large flat panel TV.  When I opened the box, the screen was shattered.  I could see a scrap mark across the front of the box where it looked like something had fallen into it.  I tried to call the seller but had difficulty getting through.  Fortunately, I paid through PayPal and when I called them they said they would refund the money to my credit card.  I asked them what I should do with the TV and they said keep it or throw it away.  I called TV repair shops to donate it, but they said they could only use parts they order new and not parts off a damaged, though new, set.  So, out in the trash it went.

P.S. I recently bought a used tuner from a vender in CA (I live in Ohio).  The vender said they didn’t have the original box or packing material but would pack it securely.  The tuner arrived in a shipping box but was not double boxed.  In place of the molded styrofoam, they wrapped the tuner in a few layers of bubble wrap.  Fortunately it arrived safely. 

buyer beware here in the UK!  
 A few months back, I sold a large pair of elecrostatics speakers on ebay for £3,500 UKP
The buyer was in a different part of the UK, so we needed to arrange delivery rather than collection.
I used Hermes which was a very reasonable price until it came to the insurance which was over £200 UKP on top of delivery but the shock to me was this didn't cover damage, only loss!
Hermes won't insure  any electronic items for damage!
They were in the double skinned original packaging and fortunately, all went well and the buyer is a now happy user of my Martin Logans and I am a happy user of new ATC SCM40As ..... (which I collected from the dealer!)

I'm not an expert but I have some legal experience. The info you received from previous replies here is valid and correct. Some folks do send broken and misrepresented items. Insurers do need to protect themselves from that. However, in my experience and common sense, if a company charges you for a service, you should have it. If there are issues that could invalidate that agreement the insurer should make that clear. Also, I often receive packages that are left at my door without a chance for me to inspect before I accept. Just be honest and follow up, I hope you get a break. 

Back a year or so ago I had purchased a used pre that was shipped from the mid-country to the east coast insured for the full price(4500). Buyer purchased new double box and packing materials from manufacturer. Package arrived and did not show any immediate signs of being mishandled. Upon unboxing and putting into the system 'something' was amiss, there was a noticeable noise coming from the unit. After a couple of emails back and forth we started a claim and I took the unit into a authorised repair shop. Turned out several of the output capacitors had the leads broken off from a impact, so it was determined that the box had been dropped on its side. FedEx paid the claim which was less than the full estimate, but would have probably covered the repair if I had not elected to replace all four of the output caps with new rather than just replacing the two that were unusable. It ended us costing me a bit, but in my estimation I got a good deal on the unit and it was worth the investment.

All in all I felt it went pretty well with the shipper