One could certainly "infer" it, but they would be irrational in doing so if they ignore the fact that there are also other factors that can support other inferences. Paying attention is definitely important, and a severe lack of it has been displayed here. Also, considering that my intuitions disagree with yours, I wouldn't want to be a "lazy sceptic" and deny "reason"
;)
Your analogy is problematic. In this case, one clearly has many reasons for avoiding the soup. Firstly, they know that bad food can make them sick which is clearly not good for them. No such evidence for the intrinsic badness of death exists. Secondly, the waiter, someone we presume to know exactly what the food is (as opposed to someone merely having some strong intuitions about the food that they never bothered to investigate), so it would be reasonable to trust them. The larger intuition that the bad soup should be avoided could be true. But it's exact nature could differ based upon our reasons, not all of which are rational.
1. I want to avoid the soup because I suddenly feel that it would transport me to hell. This makes little sense and is uncritical.
2. After having considered the clear possibility of illness and the fact that a waiter working in the restaurant surely knows the food there, I would want to avoid this soup because I do not want to incur significant harm. I could retain some of my health even if I had a bad but slightly less bad soup, and since I value my health, it would be rational for me to pick that option.
I am pretty sure that rational intuitions would drive us towards the latter choice.
A more appropriate analogy would be to consider a somewhat knowledgeable friend going with you to a restuarant that neither of you have ever visited before. You see an item labelled X on the menu and your friend immediately tells you to not eat the item because it would give you cancer. You ask your friend for reasons behind his claim and he replies that this is what he feels to be the case. Now, you could simply accept his claim at face value and perhaps abandon this restaurant that could potentially have excellent food. Or, you could start looking for evidence. Is there are evidence for some deadly food being served in your locality that immediately gives you cancer after being consumed once? Should I trust the word of my friend who, despite knowing a lot, still has little to no understanding of the food being served at the restaurant there? Ultimately, you could still decide to not eat the food, but this wouldn't be because you think that the food would give you cancer. It could merely be that you don't want to waste money on an unknown dish labelled X that you've never hears of and might not like the taste of. At worse, it could also make you sick.
What changed here was not the larger intuition of "avoiding the food", but the intuitions that were associated with it (that it would cause cancer) and consequently the reasons for going with that intuition (not wanting to waste money or become slightly I'll). Rational inquiry gave us reasons to not have a particular view about something whilst still considering it to be bad but to a different degree and for different reasons that did not have much to do with the intrinsic badness of the food (such as the purchase of the dish being a waste of money).
In my opinion, it's necessary to realise that:
1. Not all strong intuitions are correct. Good examples of this include our ancestors' fear of natural phenomena as being acts of divine punishment.
2. We could retain that overall instinct but for vastly different reasons (avoid thunder in case it hits you and causes you immense pain instead of running away from it due to a belief that it would condemn us to hell or something). Additionally, we could discard the parts of it that we know to be indefensible based upon the evidence we possess.
The difference remains vital and potent, irrespective of whether or not people see it. Also, it's peculiar to talk so favourably about certain intuitions (such as death being bad) whilst going against others (like reproduction and life being good). Arguments for antinatalism frequently involve such arbitrary double standards.
Not everybody shares the intuition that death alters us and brings us to a terrible state of affairs. If you want to accuse countless people's intuitions and rational faculties of being corrupt, then you're the one who needs to justify that claim. Prevarication and obfuscation won't help as far as that is concerned.