A pubMed search on 'intestinal permeability' returns almost 12,000 results, many of them very recent, so it's not exactly a marginal area of interest.
My reading of it is that there's a clear consensus that increased intestinal permeability / leaky gut is a thing, but it's still poorly understood and doctors aren't quite sure what to do with it. But as an avenue for exploration in chronic illness, it shows a lot of promise. Michael Maes (mentioned in the title of this subforum) found promising symptom improvement in me/cfs patients by treating leaky gut with l-glutamine, zinc and NAC. Best results are with young sufferers or those with illness < 5 years, which rules a lot of us out, but still suggests a very promising area for research. But it was quite a long-term treatment and definitely not "easy to fix" (getting back to the title of the thread).
Regarding the 'proper' name for the concept, leaky gut is just informal shorthand. A lot of this research has been carried out in non-English speaking countries. If English isn't your first language, leaky gut is a lot easier to say than increased intestinal permeability. The term has acquired a certain 'quacky' association though because some people have pushed the notion of 'leaky gut syndrome', which seems to have come from nowhere and is indeed often used to promote sketchy therapies and potions.