Where are the sources for his parents being those two? As far as I know, there isn't any. Most of this is from Ancestry trees and they are completely false (As is mostly the case).
The only thing we know really about Anthony's life prior to marriage is that according to his will of 1626, he has a brother Richard Brewin, living at Broughton Astley and a cousin John Brewin, living at Little Stretton.
The only thing I can find about a Richard Brewin/Bruan is a marriage in Broughton Astley 1621 for a Richard Brian to Elizabeth Smith.
Cousin John Brewin we can pin as the John Brewin/Bruan who baptises children at Little Stretton in the 1590s. Married to an Elizabeth, who is buried 1618 Little Stretton 'Elizabeth, wife of John Bruan'. John then is buried 1637 Little Stretton, 'John Bruan, Senior, Husbandman'. This line stays at Little Stretton and are later styled 'Gentlemen'. (I descend from this line, as well as the Wigston Magna line).
This Bruan family of Stretton also Marry to a Mary Andrews in 1608 Great Stretton, who is then buried 1614 Little Stretton, 'Mary Bruan, the wife of Robert Bruan'. It should be noted that the Andrews family of Little Stretton have a Gentry connection. They descend from the Andrews of Bisbrooke. Their pedigree can be seen in Nichols Antiquities of Leicestershire. So we can know that the Brewin/Bruan family line of Little Stretton at least, are not of Labouring status. John Bruan is also one of the witnesses to the inventory of Edward Andrews, Gentleman, of Little Stretton, 1623.
