The 12 Foot Skiff's don't have flat hulls.  The "pencil" 18s didn't have wide hulls, nor do many skiffs.

The 16 Foot Skiff, from which the term in it current sailing usage basically came, has never had a trapeze for all crew members.

The Historical Skiffs have no assy and no trap and don't have flat hulls.

(EDIT - whoops, a bit late on the last two).

Skiffs weren't even particularly fast when it came to getting into traps, historically.

The term "skiff" as we know it comes from the classes that first developed in Sydney.  The term popped up in the 1870s, in reference to 19 and 22 footers.  The "skiff" label came from the fact that these classes had limits on beam (less than 5') and hull depth (less than 20") that kept them closer to the rowing skiff in style, compared to the few bigger and beamier sandbagger type centreboarders.  The "skiffs" became the most prominent early replacements for the old "deep keel dinghies" which were basically baby yachts.

The "skiffs" were then replaced as the most prominent type by the "fishing boat" 24 footers, which had a minimum beam (not a maximum beam like the skiffs) and were originally fairly cruisey half-decker.  They were "a more beamy and weatherly craft" than the skiffs and the old painted and tarred-bottom cruiser/racer "fishing boats" ended up developing into unballasted undecked racing machines by 1876. These were kept ashore so needed no ballast to keep them afloat while on moorings.  Because they were kept ashore they could be varnished, and so for a while there was an unusual classification between 24 foot "painted boats" and the 24 foot "varnished boats".

The "fishing boats" were the most prominent of what were known as "Open Boats".  By the 1880s, the cost of the vast rigs and crews of the 24s was leading people to move into 22 Footers, which of course went down the same route to ever greater beam (50% of the LOA), more sail and more crew.  They also became horrendously dangerous, with single capsizes sometimes killing 4 to 9 people.  

The smaller "open boats", like the 14s, 10s, 8s and 6s were known as "dinghies".  All of them had the same sort of rules - only LOA was limited in the early days so beam, rig and crew numbers were vast.  However, in some regattas there were classes for "skiffs" which followed the earlier them of having maximum beam and depth, which kept them closer to rowing boats.  These did not have the same sort of regular racing as the big "Open boats" and small "dinghies".

The expense of the vast rigs and crews encouraged the formation of the first truly organised "skiff" club, which brought in the tightest set of rules ever seen in "Open boat" racing.  The club rules (later adopted and modified by the 16 Foot Skiff class) put limits on beam, depth and crew numbers, and sometimes boom length.  Sail area limits and more dimensional limits were later introduced on 16s but not 12s, which didn't really take off for decades. As one old 16 Foot Skiff designer said of the early 16s "these really were skiffs" just like rowing watermen's skiffs.  Again, what made a boat a "skiff" was the LIMITS, not the freedom.  

When the 18s developed they were called "18 Footers" and were one of the unrestricted "Open Boat" breed.  They followed the normal route to massive rigs and crews, while the 16s were developing into a much more efficient style under their restrictions.  This caused a huge ruckus when "skiff type" skinny lightweight boats with flatter sterns (ideas developed in the 16 Foot Skiff class) moved into the 18s and showed them what planing meant.  There are pages and pages where fans of the spectacular big-rig old-style 18s sling hate at the "skiff type" 18s, saying that it wasn't speed or open rules that mattered, but just putting on a good show for the crowds in the ferries. 

The term "skiff" remained largely restricted to 16s and (to a lesser extent) 12s for decades - people like two-time world 18 Footer champ Peter Mander never used the term in his autobiography, referring to them in the usual style of his era just as "18 Footers."  It was only in the '70s and '80s that the term started to get used to refer to a general type of boat.  The idea that people had "8 foot Skiffs" and "18 Foot Skiffs" in the 1800s and 1920s is just applying a modern term to boats whose owners would have thought it a joke.

But throughout the whole evolution of the word, the "skiffs" (not just the 8s, 18s, 22s etc but also the 16s) have always had more righting moment and more sail area per foot than anything that was called a "dinghy" in the northern hemisphere.  There has never been (and still is not, as any look at an 18, a 16 and a 12 will show) any such thing as a "skiff shaped hull".  Some are rounded, some are flat, some have chines, some don't.  They have often been quite retrograde and sometimes slow, at least compared to their sail area and cost.  But the basics of a very large rig and high righting moment have been there since the 1800s, and still are today.

Personally I dislike the term "skiff" being thrown at anything fast, since that makes the term meaningless and also ignores the enormous importance of conventional dinghies in the development of the modern sailing boat.  It's a bit like referring to every fast car as a "Porsche" or "Formula One", even if it's a Mercedes or a world champ rally car.  It's about as sensible as it would have been to call Contenders "Flying Dutchman" as a generic term just coz it's kewl and them FDs are sick boat, bro. 

All of the above is from primary sources.  While I liked Frank, his history is often incorrect and quite often (as in his claims about the arrival of the catboat Una in the UK, and much of his information about the sandbaggers) it is completely the opposite of what actually occurred.