Why are spiders called spiders?

This is probably a repost, but did some research that follows. If anyone knows of a better explanation, I'm all ears. The whole explanation, taken from two web sites is below. The abstract version: Phaetons were a type of owner driven horse drawn carriage with a top that folded down. In the 1860's, in America, the Spider Phaeton was designed. The distinguishing feature of a Spider Phaeton was how open, delicate and sporty it was compared to the Phaeton. Eventually, the Spider Phaeton design became very popular in Europe also. While a lot of carriage names, like Phaeton and Cabriolet, were adopted early as car names, the Spider name was not used until Alfa Romeo adopted this name for the Pininfarina designed Giulietta.

http://www.caaonline.com/caa_content.asp?PageType=Dept&Key=15&MCat=10
Phaetons come in all sorts of varieties and sizes. It is a term that often confuses the casual visitor to carriage museums and collections. Indeed it should, because it was such a widely, inconsistently used term that derives from the Greek (Phaethon, son of Helios, who drove the Chariot of the Sun with such careless abandon that Zeus struck him down with a lightning bolt to prevent him from destroying the Earth with fire). The term was first applied to classify a carriage during that 16th century period in France when it was so fashionable to use classical pseudonyms. Usage of the term spread quickly to England and America. There are few distinguishing characteristics that can restrict the use of the term -- perhaps only that it is an owner driven vehicle and that it nearly always includes some sort of top that would shelter, at least, the driver. The name was applied to both large and small carriages that might be drawn by one or more horses. Actually, manufacturers used the term extremely loosely and it gains one little to consider why any particular vehicle might have been called a Phaeton. The Spider Phaeton was so named, however, because of its extremely delicate lines and lack of bulkiness. Notice the rear seat for the groom and how open and delicate it looks compared to the one on the Stanhope Phaeton that is included in this tour. The Spider Phaeton was originally designed in America in the 1860s, but became very popular in both America and Europe in the last decade of that century. Carriages of similar design were manufactured by many companies.

http://www.lyles.co.uk/newsite/site/alfabadge.asp?pageid=93
Alfa Romeo Spider, but why Spider?

The Italian for Spider, the hairy eight-legged creature that lives in your attic and reduces nervous people to cowering wrecks, is ragno. But no Alfa Romeo Ragno has ever been marketed. Nor does the word derive from the ugly Britslang for a hood - top. So just how did Alfa Romeo’s open two-seaters come to be called Spiders?

It all goes back to the days when horse power, not horsepower, ruled the road. A ‘spider’ was a light, four-wheeled horsedrawn carriage with a compact passenger compartment and uncommonly high wheels. It was more properly called a ‘spider-phaeton’ and was one of the more dashing vehicles in the equine cart-park.

Unlike phaeton, cabriolet, sedanca deville, landau, victoria and brougham, but along with gig and trap, the spider name didn’t make the crossover to the emerging car world at the turn of the century. Most of the those old-time names were adopted by American manufacturers but, whenever they came up with a car that might have fitted the spider concept, they called it something else. Mercer’s sporty 1912 contraption, or instance, was christened a Raceabout, Pierce-Arrow’s equivalent a Runabout.

Alfa Romeo’s gorgeous two-seater sports cars of the 1930s, the 1750 and 2300 models, usually sporting lithe, lightweight coachwork made by expert craftsmen at Carrozzerie Touring or Zagato, seem natural born spiders. But they were never known as such at the time.

It was the same with the early open two-seater Ferrari 166. That was always a Barchetta - Italian for ‘little boat’. Other delicious Italian open sports cars that could have qualified for the spider tag include the Lancia Aurelia (rather boringly called the B24), the Siata 1400 (Grand Sport), and the OSCA (MT4).

It wasn’t until 1954 that Alfa Romeo plundered the history books, adopting the name spider for its open Giulietta, the pretty Pininfarina-styled and built sports car remembered by many as the one Edward Fox resprayed so perfectly in a forest clearing during the movie Day of the Jackal. The name suited the car perfectly, with its intimate cockpit and wheel-at-each-corner stance. It also gave the car a special identity, imbuing it with the nervous energy and web-spinning dexterity - the pest-munching usefulness - of its arachnid namesake.

 

Sounds like you are close to the full story. It seems that the black cloth on top of four ribs, with open sides, made it look a bit like a spider (see below). That sounds right. Second paragraph below complicates things.

This is from http://dictionary.sensagent.com/spyder/en-en/

As with other automotive terms, the term derives from horse-drawn carriages. A "spider" was a lighter version of a phaeton, having narrower, spindly wheels and two-seat accommodation. The name implied an extremely rudimentary top mechanism originating from a small two-seat horse-cart with a folding sunshade made of four bows; with its black cloth top and exposed sides for air circulation it resembled an eight-legged spider. This term was subsequently applied to automobiles.

Alternatively, a native Italian who has had no English influence in the pronunciation would pronounce "spyder" or "spider" as speeder. Thus a car labeled by an Italian car manufacturer as "Spyder" or "Spider" is intended to be simply a "speeder" or a sports car. (Aston Martin used to have a car labeled "spyder" but now have a model labeled "Volante", an Italian word that translates into English as "speeder".)