altered garments

The theory is not so much that the dresses we are seeing are largely cut down, but that these are the dresses that were not able to be cut down, since they were already the proper size for the smallest women; it's somewhat assumed that women who wore the heavily-altered dresses of other women were of a lower class, purchasing on the secondhand market and then wearing the dresses fully out themselves. Extant clothing that shows signs of alteration are usually let out in the side seams, darts, or sleeves, or else left the same size and made more fashionable (sleeves changed from pagoda to coat, skirt panels gored, etc.). (Or else completely reworked, as with this silk gown, which was originally made in the eighteenth century and was taken apart and remade in the 1840s.)

people used to be smaller

This is a very, very difficult topic. Simply put: we don't have the kind of information we need to make this call. For instance, in the mid-twentieth century MetLife put together a table of average weights for various age- and height- groups of men and women, which were reproduced in all kinds of publications at the time and has been used as representative of all Americans at the time. But these heights and weights are a) self-reported and b) only representative of the people allowed to purchase a Standard Policy; people deemed too thin or too fat were only allowed Substandard Policies. Likewise, in 1939 and 1940, the Department of Agriculture collected self-reported measurements from white female volunteers in order to put together a standard sizing system for ready-to-wear clothing and found that the average white American woman was 5'3" and 125 lbs; since they paid for measurements, though, they may have drawn overly from the most impoverished segment of society (and remember, this is during the Great Depression). As a result, while we know that the proportion of Americans who qualify as "obese" has increased since the 1970s, we don't have good enough information to say what was seen as a normal (rather than statistically average) weight in the past. Street and family photos of the 1950s, for instance, show many people who look like they would be considered plump or overweight today - but extant vintage clothing and sewing patterns in sizes larger than a modern 8 are still incredibly hard to find.

Certainly there were more people who were thin from malnutrition, and certainly people found it easier to keep weight off with the sort of food they had access to and more need to walk to work, to do shopping, etc. But these dresses are disproportionately numerous today in comparison to when they were being worn.

corsets

We tend to fixate on the waist measurement, and a small waist measurement for a dress does imply an ordinary body with the waist cinched in by a corset. It's important to look at the bust measurement as well (and sometimes hip, depending on the period) in order to get a more accurate view of the body that wore the garment. Some time ago, I measured the patterns in Norah Waugh's Corsets & Crinolines and Jill Salen's Corsets to find out their dimensions:

Book	date	bust	waist	hip
Corsets & Crinolines	late 1820s	30	20	30
1844	34	24	34
1860	28	19
1873	28	20	32
late 1880s	30	18	26
mid 1890s	30	19	33
1902	34	20	30
1911		20	26
1904	35	28	32
1918		22	34
1925	33	31	37
Corsets	1830s	33	22	31
1840s	38	26	32
1860	33	22	30
1885	31	24	30
1890		21	26
1890	31	22	28
1890s	30	21	32
1890s-1900s	39	34	48
1890s	34	27	32
1890	32	22	28
1900s		22	26
1900s		24	31
1914		21	25
1917	30	23	31

(Spaces reflect a corset either being cut under the bust or very high on the hip. Also bear in mind that these were intended to be worn with a 1"-3" gap in the lacing in back.)

As you can see, tiny waists tend to go along with small busts and narrow hips. It's likely that many women at the lower end of the scale were not getting that much waist reduction from their corsets in the first place - pushing body fat down to the hips and stomach is the biggest thing a corset down to narrow the waist.