A Student's Introduction to English Grammar, p. 90:
The determiner position in an NP [noun phrase] is usually filled by one of two kinds of expression.
In all the examples so far it has been a determinative [a word like the, a, this, some, or three], and some of these can be accompanied by their own modifiers, making a determinative phrase, abbreviated DP.
In addition, the determiner may have the form of a genitive NP.
Examples, with the determiners underlined [bolded], are given [below]:
DETERMINATIVE
*the city
**some* rotten eggsDP
*almost all politicians
**very few* new booksGENITIVE NP
*her income
**the senator's* young son
p. 109:
As a determiner, the genitive is always definite. Note, for example, that [one patient's father] corresponds to *the father of one patient, not **a* father of one patient.
See also the Wikipedia determiner and genitive case articles.
Note, for example, that [one patient's father] corresponds to the father of one patient, not a father of one patient.
Hm. So how do you express the concept of an undetermined relative of some patient? The text you quoted would say that [one patient's relative] means the relative of one patient -- how do I express a relative of one patient?
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
Of course, for "every Monday", the last one should have been dated July 22-28. *cough*