Not necessary, because the argument is based on a comparison between the people who drank tea, but no coffee, and the people who drank coffee, but no tea. If there were other kinds of people in the study, such as those who drink both, or those who drank something else, those people aren’t part of the comparison relied on in the premise.

Not necessary, because other health benefits besides those related to the immune system aren’t relevant. The argument concerns the cause of the tea drinkers’ faster immune response time compared to the coffee drinkers.

Necessary, because if it were not true — if drinking coffee DID cause the blood cell response time to double — than the true explanation for the tea drinkers’ faster response time doesn’t have to be that tea boosted defense. It could instead be that coffee slowed defenses, and tea just had no effect.

Not necessary, because if coffee drinkers ARE more likely to exercise and eat healthily than tea drinkers, that arguably would strengthen the argument, because we’d expect the coffee drinkers to have a stronger immune system. So if they ended up having a slower response time, that lends support to tea having a potential benefits to the immune system. Also, we don’t know that what applies to coffee drinkers “in general” applies to people who drank coffee for the purpose of the study.

Not necessary, because we’re concerned with what accounts for faster immune response time. Coffee and tea might share some chemicals that fight disease — that wouldn’t suggest we can’t observe a difference in immune system response time or that something about tea can’t help the immune system.