Qualitative research needs to be holistic, as you have discussed. Qualitative studies are concerned with soft sciences, which investigate social phenomena like illnesses; hence, qualitative research methods are ideal for collected vast and valuable information. They should therefore touch on all possible aspects of a population, which concern the issue being investigated.
Besides your discussion on logic, I note that qualitative research designs are informed by indictive logic. For instance, a hypothesis is developed after collecting data and preliminary analysis (Sutton & Austin, 2015). Such a hypothesis is ideal for making detailed descriptive conclusions about a phenomenon.
Also, the logic of sampling is that sample units are used to represent a wider population. From these, statistical means are used to judge the characteristics of all members of a population. Both the purposive and snowball sampling methods you have discussed are practical for qualitative research methodologies.
Sutton, J., & Austin, Z. (2015). Qualitative Research: Data Collection, Analysis, and Management. The Canadian Journal Of Hospital Pharmacy, 68(3). doi: 10.4212/cjhp.v68i3.1456