Looking at the paragraph you mention, there's not really one source you can point to that is the basis of his point. Initially, I believed you (and by extension Fisher) were discussing the status of blacks in the early seventeenth century. The section under discussion is post-Bacon's Rebellion, when slavery was becoming better established in the colony. I'll try and unpack what I believe Fisher is arguing in the quote:

A slave was rarely called a slave in the American south by his master. Slaves were referred to as "my people," "my hands," "my workers," almost anything but "my slaves." They were made to dress like English farm workers, to play English folk games, to speak an English country dialect, and to observe the ordinary rituals of English life in a charade that Virginia planters organized with great care.

So, first off, Fisher is wrong about his population estimates of the Virginia slave population. This is not entirely his fault, as he was writing before advances in our understanding of the slave trade and Virginian demographics were published. The best recent estimate of the black population in Virginia in 1700 is about 16,000, a figure supported by the Slave Voyages Database and the work of Greg O'Malley on the inter-colonial slave trade (O'Malley, "Beyond the Middle Passage," WMQ 2009, pp. 139-141; McCusker, Historical Statistics of the United States, Millennial Edition, 5:653). Fisher’s estimate of 6-10,000 (and he states the lower is more correct) underrepresents the scale of the shift from white indentured to black slave labor.

What Fisher is trying to explain is the destruction of African culture among the enslaved, and in his argument, the destruction was quick and thorough. He is explaining that Africans imported into Virginia were not provided or allowed to wear the clothing they would traditionally have worn in Africa. We know this because planters would provide their slaves with English style garments – shirts, pants, caps, etc. In Africa, a more common manner of dressing was to take a broad cloth about 2 meters long and wrap it around the body, instead of cut and sewn pieces (Miller, Way of Death; examples of slaves clothing in America include the Virginia runaway advertisements, This, the Correspondence of the Three William Byrds of Westover, Bruce’s Economic History of Virginia, 2:105-106, or check Kulikoff, Tobacco and Slaves). Hugh Jones, a minister in Virginia claimed that recently imported slaves spoke in “various harsh jargons”, while slave born in Virginia “talk good English, and affect our language, habits, and custom.” (Hugh Jones, The Present State of Virginia 1724, quoted in Kulikoff, “The Origins of Afro-American Society,” WMQ 1978, p. 226).

Fisher is getting his views from authors like Jones, and from secondary authorities cited in Kulikoff, such as Mullin, Flight and Rebellion. Since these authors have written, most scholars acknowledge that while slaves may have spoken English, worn English clothing, etc. they developed their own uses and cultural meanings for English objects. Slaves decorated their clothing in their own manners, with trims, buttons, and ribbons; they gave themselves nicknames or surnames, so that in runaway advertisements, masters would state things like “Goes by Stephen Butler” (Maryland Gazette, April 2, 1772). Fisher may be right that blacks were coerced to accept aspects of English culture, but that did not erase their ability to adapt and create new meanings for themselves.