No, children diagnosed with ADHD are not just immature. ADHD is a medically diagnosed condition that should be managed with treatment under a doctor's supervision. I believe there are many options to treat ADHD, based on severity of the case, but age is not a limiting factor in ADHD diagnosis.
While there has been something of a doctor's fad of diagnosing children who are simply 'naughty' with ADHD over the past decade (and prescribing them with very strong drugs) it is not the case that all children diagnosed with ADHD are simply immature. ADHD is a real condition that can be very detrimental to a child's education unless it is properly dealt with.
The scientific evidence is clear that there are structural, molecular and functional differences between the brains of ADHD sufferers and healthy controls. Having said that, it may be the case that ADHD is over-diagnosed by doctors who rely on subjective behavioural measures to make a diagnosis, rather than on brain imaging evidence.
This is especially true in the USA, where the profit-driven healthcare system is set up in a way that often forces medical professionals to use the cheapest techniques possible, even if they are not evidence-based and lack diagnostic value.
There is definitely a concern that we are over-medicating the problem, but just because we are over-medicating it doesn't mean it's not a problem. It is possible that some with ADHD may be able to overcome or reduce their symptoms with talk therapy and other techniques. ADHD should be taken seriously and one way to do that would be to have a comprehensive, well measured approach to dealing with it.