My go-to phrase: "Even if there were no real difference, we would see a result like this X% of the time anyway."
That is what a p-value means, feasibility aside. There are also more intuitive ways to think about it, "false-positive rate" being one.
Hmm, p-values are data-dependent random variables. Do this simple experiment in R where the null hypothesis of no difference is as true as can be:
replicate(2,t.test(rnorm(10),rnorm(10))$p.value)
For example, I got:
[1] 0.8446991 0.3935238
So, the p-value can vary wildly (actually will follow a uniform(0,1) distribution) even if there were no real difference.
Experimenter A would tell you that "we would see a result like this 84% of the time anyway" and experimenter B would say 39%. If enough experiments are performed, eventually someone will calculate a very small p-value. So which experimenter should we listen to? Which experimenters should bother sharing their results? All are correct.
In other words, what should be done with that information about "even if there were no difference"? How should it affect our behavior, decisions, and beliefs?
Suddenly, the abysmal state of nutritional epidemiology makes sense. How many labs do you suspect are running "red meat = death" studies?
Sadly, it only goes to point out the sad state of contemporary science. Especially in terms of nutrition, the only way to stay sane is to stick to the good old street-fighting Bayes - if popularly consumed product X was leading to cancer in any way relevant to your life, you'd see people dropping like flies all over the place.
I suspect you already know this, but it bears repetition, if only because it keeps us optimistic: science is a process. Even nutritional epidemiology will eventually find its way out of the abyss. :)
And yes: the ol' jellybean XKCD is quite a propos.
So as it stands now, I classify every new and contemporary (younger than 10 years) study in psychology, sociology and nutrition as "not science" and "quackery" by default, until proven otherwise. I also assume that any science news reporting in any field is an outright lie with an agenda. Rarely do I see a counterexample. Seriously, science reporting does way more harm than bad research itself.
I'd encourage you to be careful in dismissing the entirety of experimental psychology (full disclosure: I'm a cognitive neuroscientist, which is what a psychologist calls himself when he wants to distance himself from social psych).
The reproduction crisis doesn't touch all fields of psych in equivalent ways. When you reject the field as a whole, you're also rejecting stuff like this: http://cavlab.net/?lang=en