The cancer example is plausible, but I am not sure you would always win.

In that case you are asking for help for a specific reason. They “get to feel good about helping solve your problem”.

Your deception deprives them of their having done something good with their money - which is the tort.

In OP’s instance, he was saying that he had a birthday and you are giving him a gift.

Not the same - you can make the same argument, but it is even thinner gruel.