The Early History of the Kilt (http://albanach.org/kilt.html) and Reconstructing History (http://www.reconstructinghistory.com/scottish/18thckilt.html) quote modern scholarship disputing this story with reference to earlier illustrations of the small kilt.
The small kilt developed into the modern kilt when the pleats were sewn in to speed the donning of the kilt.
Military use and proscription
From 1624 the Independent Companies of Highlanders had worn kilts as government troops, and with their formation into the Black Watch regiment in 1740 their great kilt uniform was standardised with a new dark tartan. After 1745 the Government decided to form more Highland regiments for the army in order to direct the energies of Gaels, that "hardy and intrepid race of men". In doing so they formed effective new army regiments to send to fight in India, America, and other locations while lowering the possibility of rebellion at home. As a means of identification the regiments were given different tartans. These regiments opted for the modern kilts for dress uniforms, and while the great kilt remained as undress uniform this was phased out by the early 19th century.
In 1746 after the last Jacobite campaign the "Dress Act" outlawed all items of Highland dress including the new kilts (with an exception for army uniforms). The ban remained in effect for 35 years. and the traditional way of life throughout the Highlands was destroyed.
The revival of the kilt
Although the kilt was largely forgotten in the Scottish Highlands, during those years it became fashionable for Scottish romantics to wear kilts as a form of protest against the ban. This was an age that romanticized "primitive" peoples, which is what Highlanders were viewed as. Most Lowlanders had viewed Highlanders with fear before 1745, but many identified with them after their power was broken. The kilt, along with other features of Gaelic culture had become identified with Jacobitism and now that this had ceased to be a real danger it was viewed with romantic nostalgia. Once the ban was lifted in 1782 Highland landowners set up Highland Societies with aims including "Improvements" (which others would call the Highland clearances) and promoting "the general use of the ancient Highland dress". The Celtic Society of Edinburgh, chaired by Walter Scott, encouraged lowlanders to join this antiquarian enthusiasm.
The kilt became identified with the whole of Scotland with the the pageantry of the visit of King George IV to Scotland in 1822, even though 9 out of 10 Scots lived in the Lowlands. Scott and the Highland societies organised a "gathering of the Gael" and established entirely new Scottish traditions, including Lowlanders wearing the supposed "traditional" garment of the Highlanders. At this time many other traditions such as clan identification by tartan were developed.
After that point the kilt gathered momentum as an emblem of Scottish culture as identified by antiquarians, romantics, and others, who spent much effort praising the "ancient" and natural qualities of the kilt. King George IV had appeared in a spectacular kilt, and his successor Queen Victoria dressed her boys in the kilt, widening its appeal. The kilt became part of the Scottish national identity.
The Kilt Today
Kilts have become normal wear for formal occasions, for example being hired for weddings in much the same way as top hat and tails are in England or tuxedos across the pond, and can be worn by anyone regardless of nationality or descent.
The modern tailored kilt is box-pleated or knife-pleated, with the pleats sewn in and the lower edges reaching not lower than the centre of the knee-cap. Nowadays a lighter weight of cloth tends to be used. The kilt is traditionally for men only, although in the modern era, long women's dresses patterned after kilts do exist, and women pipers frequently wear kilts. Kilten skirts for girls are also worn.
As with any other form of dress, the kilt is subject to the vagaries of fashion. Since the 1980s, kilts have appeared in such materials as leather and denim. Single colours have also been used in place of tartan, particularly by people without Scottish links in countries such as Ireland or the United States. While these garments may be disliked by traditionalists, they provide evidence that the kilt still has a place in the modern fashion world.
As a kilt has no pockets, it is worn with a pouch called a sporran. Originally this was a soft deer skin pouch, but with the development of military uniforms elaborate hard leather sporrans came into use, often with decorative silver tops and white hair facings with large tassels. A decorative silver kilt pin adds weight to the loose bottom corner of the kilt.
A small dagger called a Sgian Dubh may be worn in the tall stockings which form part of the standard clothing worn with a kilt. Shoes are usually leather brogues, sometimes with open lacing.
Nowadays a special jacket is usually worn with the kilt. This is often in green tweed, but with the kilt as formal dress a black "Prince Charlie" jacket is usual.
With some full dress uniforms a plaid is added in the form of a pleated cloth in the same tartan as the kilt, cast over the shoulder and fastened at the front with a plaid brooch.
A good rule of thumb is that kilts should be worn without underwear in daily use, but with it for dancing (when a light kilt may fly up). In practice, underwear is not needed for a fully lined kilt, but may be preferable for an unlined woollen kilt to prevent chafing. In the end whether or not underwear is worn on any particular occasion, is up to the weather, the company, and the individual wearer.
Whatever decision is made, what a Scotsman wears under his kilt is, traditionally, his own business and generally, Scotsmen will be at pains to keep it so. Thus the reply to a question on the topic may hint at the answer but should never state it outright. A good standard reply when asked, is that, "Nothing is worn under the kilt. It's all in perfect working order".