I think the following additional criteria should be considered when looking at these questions:
Generally studies look at a particular condition. For example, they might examine whether cucumber triggers asthma. As such, it is very difficult to prove that cucumber is healthy - but easier to show there is no evidence it causes a particular disease. (Yes, epidemiological studies could point to high cucumber consumption as being correlated with higher mortality but it is difficult to show causality.)
We should accept claims that specify a particular medical condition that the foodstuff is said to cause or cure, but should consider closing questions that leave it open-ended as "healthy" or "unhealthy".
The Dose Makes The Poison
Without a clear indication of how much of a substance is being consumed, it is largely meaningless to say it is healthy. We should accept claims that specify how much (e.g. 8 glasses of water per day), but should consider closing questions that are open ended (e.g. is eating beetroot healthy?)
Compared to a balanced diet, eating exclusively hamburgers is likely to increase mortality.
Compared to starving, eating exclusively hamburgers is likely to decrease mortality.
For people with cardiovascular risks, eating sodium-rich foods is dangerous. For youths, it may be fine.
Salted roasted peanuts may generally be considered harmless...
... unless you have an allergy
... or cardiovascular risks
... or obesity
... or they has been contaminated
... or they have been burnt
... or they are being served by a bar to encourage overconsumption of alcohol
... or they are not being consumed in moderation as part of a balanced diet.
It isn't appropriate to declare peanuts to be unhealthy (unless there is another risk I am unaware of) but nor is it appropriate to declare them healthy.
We should only accept claims that specify the audience the advice is aimed at, and it is clear what the food is replacing in the diet - i.e. what would the 'control' diet be?
Note: Good answers should address the size of the risks to allow better decision making. I accept that chocolate cake is not the healthiest choice on the menu; I consume it in moderation after accepting these risks.