The commonly accepted legend, a legend of lengthy tenure, is that 'bootleg' used in the general sense of 'illicit trade in liquor' originated from the use of bootlegs as a place of concealment.
However, that origin legend has at least one serious competitor. The competitor, in addition, is as old as the previously known attestations for 'bootleg' in the specified sense, and so antedates the competing legend ascribing the origin to 'bootlegs used as a place of concealment'.
Possible Origin
To illustrate the competing origin legends, I include the relevant citations. In OED Online, in an entry for "boot-leg | bootleg, n." not fully updated since its original publication in 1933, the sense and first attestation (known to OED) are given:
2. attrib.
a. With reference to illicit trading in liquor. Also ellipt. Cf. boot-legger n. orig. U.S.
a 1889 Omaha Herald (Barrère & Leland), There is as much whisky consumed in Iowa now as there was before,..‘for medical purposes only’, and on the boot-leg plan.
["boot-leg | bootleg, n.". OED Online. December 2016. Oxford University Press. http://www.oed.com/view/Entry/21545 (accessed January 09, 2017).]
The Online Etymology Dictionary elaborates, as quoted in the next paragraph, but does not differ substantially from the meaning and date provided by OED. Note, however, that while Etymonline explicitly ("from the trick") favors an explanation of the origin, OED, as cited above for 'bootleg', does not make any such claim.
As an adjective in reference to illegal liquor, 1889, American English slang, from the trick of concealing a flask of liquor down the leg of a high boot. Before that the bootleg was the place to secret knives and pistols.
The date given for the attributive sense of 'bootleg' is before (= a) 1889, and in OED the source is cited as the Omaha Herald, as quoted in Barrère & Leland. Barrère & Leland's A Dictionary of Slang, Jargon & Cant was published in 1889, but the quote from the Omaha Herald must be at least as old as the quoted article's reprint in the San Francisco Chronicle (San Francisco, California) of 28 Oct 1886 (behind paywall):
By using the wealth of primary source material now available (but not, presumably, available to OED at the time they developed the entry shown in the foregoing), I was able to find two 1886 uses, not of 'bootleg', but of 'bootlegger'. One of those uses, from The New North-West (Deer Lodge, Montana) 12 Mar 1886 (behind paywall), promotes the 'bootleg used as a place of concealment' origin legend:
The other 1886 use I found does not promote any origin, being merely a mention of jail sentences given to particular bootleggers in Kansas.
Now, the OED entry for "bootlegger, n." does promote the 'bootleg as a place of concealment' origin legend, but that legend is promoted as part of the sense of the word as used in and after 1889, rather than as the origin of the word:
One who carries liquor in his boot-legs; (hence) an illicit trader in liquor.
1889 Sanger Rep. in J. B. Thoburn Hist. Oklahoma (1916) I. 223 Liquor dealers (or as they are called here ‘boot-leggers’).
1890 Voice (N.Y.) July 17 The ‘boot-legger’ is a grim spectre to the anti-Prohibitionist... He is a man who wears boots in whose tops are concealed a flask or two of liquor.
["boot-legger, n.". OED Online. December 2016. Oxford University Press. http://www.oed.com/view/Entry/280116 (accessed January 09, 2017).]
Probable Origin
Barrère & Leland's entry in A Dictionary of Slang, Jargon & Cant, cited as the source of the Omaha Herald quote by OED, promotes an alternative origin of bootleg:
Boot-leg plan (American), by evasion or trickery, in reference to the saying that "the boot is on the other leg," i.e., not as one would naturally understand the assertion.
The explanation of the origin given by Barrère & Leland, that 'boot-leg plan' is "in reference to the saying that 'the boot is on the other leg'", has more chronological support than the competing origin legend.
The first use of 'bootleg' that I could find using contemporary primary source material databases is this from The Council Grove Republican (Council Grove, Kansas) 16 Nov 1844 (behind paywall):
This use, in a tongue in cheek satirical article, as can be seen from the context, precedes the earliest use cited by historical and etymological dictionaries by 44 years. The appearance of 'bootleg' without explanation suggests the sense intended is known or can be derived by astute readers from the context.
In addition, the sense of the 1844 use, that is, generally, 'illicit trade in liquor', is not only at odds with 'boot-leg' in the sense of 'boot-leg coffee' and 'type of large beer stein', it antedates the earliest uses I could find of those, as follows.
For the latter, the 'beer stein' sense, the earliest use I could find is the 1886 use cited in the question. The former, 'boot-leg' in the sense of 'boot-leg flavored coffee', appears somewhat earlier, in 1868/1863:
From The Courier-Journal (Louisville, Kentucky), 10 May 1868, in a reprinted article dated 1863 about a visit to New York's City Prison.
Background Information
The saying mentioned by Barrère & Leland, "the boot is on the other leg" (equivalent to our contemporary saying, "the shoe is on the other foot"), attested as early as 1533 in OED ("T. More Debellacyon Salem & Bizance ii. xv. f. xxxvv, That their wordes shold haue two senses, & one bote serue for eyther legge.") was relatively common in the popular press in the early 19th century, prior to the 1844 use of 'bootleg' with reference to illicit trade in liquor in New England.
It should also be observed that the "first state prohibition law was passed in Maine in 1846" (from "Prohibition", Encyclopædia Britannica, 2016), that is, two years after the 1844 use shown in the foregoing.
