I can't even bring myself to ask "what is the evidence" because, as discussed a year ago in the profile comments, there's obviously none and this linkage (to an English peer who is documented as having had no children, apparently? and whose name doesn't even match) is just silly.
Per Walter Goodwin Davis (Massachusetts and Maine Families, vol. 3, pp. 62-3), Francis' origin and arrival and parentage aren't known.
The much-too-specific birthdate (18 Jan 1617) at least has a source (though the source says 1618): I found it in Ames, John D. "A Genealogy of the Nurse Family for Five Generations." Putnam's Monthly Historical Magazine, Vol. 1 (1893), p. 96 (on Google Books). But the claim is unverifiable, and works from this era aren't trustworthy on those kinds of details.
Also per the comments, there is no such place as "Yarmouth, Bristol, England", poor Francis' currently-listed "birthplace".
Propose detaching the parents and changing the birthplace to "England". Further propose adjusting the birthdate to "about 1618" which is supported by some depositions and his recorded age at death (per Davis).