In the context of my OP, it is a good assumption. In fact, it's a logical conclusion to make.
P1. I don't like private healthcare because some hospitals can deliberately keep patients ill to make more profit and the healthcare might not be affordable for everyone.
P2. As a result of a P1, I support a state-owned health service.
P3. Many people starve (homeless people and people of very low incomes) because they can't afford food and drinks. Also, however unlikely it may be, it's not impossible for several food and drugs companies to collude together to make the masses ill to make more profit.
C. If P1 and P3 are similar situations and P2 was the response to P1, then it is a logical conclusion to also want food and drink production and import to be gov't-owned.
You can't have your cake and eat it. It's absurd to want public healthcare for a set of reasons but not want public food production, even though the reasons for supporting public healthcare are exactly applicable to supporting public food production and imports.
You've cleared up that's not impossible for drug companies to make people ill for profit (although the regulations on these things are ridiculous and it's practically impossible, although that will change I'm sure) - but food companies can't make people HUNGRY for profit. What they can do is overcharge, but there's too much competition for that to be an effective plan, especially with food being such an abundant resource.