Where does the phrase "doctored" originate?
The earliest Google Books match for an instance of doctored in a transitional (or perhaps post-transitional) sense between "amended" and "adulterated" appears in William Marshall, The Rural Economy of Glocestershire; Including Its Dairy: Together with the Dairy Management of North Wiltshire, and the Management of Orchards and Fruit Liquor, in Herefordshire, volume 2 (1789):
Men in general, however, whose palates are set to rough cider, consider the common sweet sort as an effeminate beverage; and rough cider, properly manufactured, is probably the most generous liquor; being deemed more wholesome, to habits in general, than sweet cider:—even when genuine. That which is drank, in the kingdom at large, is too frequently adulterated. The "ciderman" cannot afford to lose a hogshead: if it will not do, it must be "doctored": or if sound, it may not be sweet enough for the palate of his customers; nor high enough coloured to please the eye; but the requisite colour and sweetness, he finds, are easily communicated.
This is evidently the sense of "doctored" that appears as OED definition 3 in tchrist's answer:
3. fig. To treat so as to alter the appearance, flavour, or character of; to disguise, falsify, tamper with, adulterate, sophisticate, ‘cook’.
And yet it is not so very distant from the OED's definition 2b (again as quoted in tchrist's answer):
2b. transf. To repair, patch up, set to rights.
The line between "repair, patch up, set to rights" and "disguise, falsify, tamper with, adulterate" is not clearly demarcated—certainly not if you are a ciderman stuck with a hogshead of cider that no one will buy in its present state. Rather, it's a continuum that begins innocently enough with making improvements that are to everyone's advantage, and only gradually gives way to disguising an inferior product without acknowledging its original shortcomings or—in the worst case—without actually improving it at all. In this respect, it mimics the difference between sound medicine at one end of the continuum and quackery at the other.
The adjective doctored derives from the figurative use of the verb doctor, meaning per the OED:
To treat so as to alter the appearance, flavour, or character of; to disguise, falsify, tamper with, adulterate, sophisticate, ‘cook’.
The first citation is from the 18th century.
In case it helps you see how these things developed, here from the OED, minus the citations, are all the senses given for doctor verb, including this one:
1. trans. To confer the degree or title of Doctor upon; to make a Doctor.
2a. To treat, as a doctor or physician; to administer medicine or medical treatment to.
2b. transf. To repair, patch up, set to rights.
2c. To castrate (an animal).
3. fig. To treat so as to alter the appearance, flavour, or character of; to disguise, falsify, tamper with, adulterate, sophisticate, ‘cook’.
4. intr. a. To practise as a physician. (Usually in vbl. sb. or pr. pple.)
4b. To take medicine, undergo medical treatment.
Hence ˈdoctored ppl. a., ˈdoctoring vbl. sb.; also ˈdoctorer, one who doctors.
It should be pretty clear how the straightforward sense 2a turned into the transferred sense 2b, and thence to sense 3 by figurative extension.
This shows why it is important that senses be listed in the historical order that they came into the language, not merely by order of each sense’s currency or popularity.