I don’t understand why you would use it though. And invasion implies violence. We simply cannot be sure if there was any violence at the level of calling it an organised invasion.
Why does it have to be "organized"?
Respectable historians don’t say Anglo-Saxon ‘invasions’, where a very similar situation to Bronze Age India was occurring. They use migrations.
In England it was a population that clearly used violence in the process of settling their new territories, this much is indisputable. There is no need to demand it being "organized".
Likewise across the rest of Europe. And it wasn’t a an assimilation. It was these various bands of primarily male migrants striking deals and marrying into the power structures of the area. They then diffused their language slowly from the top down.
This is not the case, genetics have already proven than in India there was a big enough demographic component to the indo-europenization, This is even more so depending on how you interpret the genetic makeup of the original newcomers to have been(already mixed with Central Asia or "pure" Yamnaya/Andronovo-like people? probably the earlier, making the demographic impact even bigger), but even the most conservative estimation would give an impact of more than 20% outside ancestry for most of the Indus and Ganges basin and more so for the northern Indus valley.
And while I agree it wasn’t completely peaceful the imagery behind the words of ‘Aryan Invasion’ is of fair skinned nomads smashing the cities of dark-skinned aboriginal inhabitants and subjugating them via caste in perpetuo. Thus it’s not about semantics, it’s about undoing many years of post-colonial myths that have left such a bad blood in the locals that they find it hard to come to terms with their history.
You are arguing with 19th century dead scholars, if we strip your caricature of any further meaning and ideologies, we can actually say that Aryan invasion was a process where Indo-Aryan speakers, which if we had to mention were probably lighter than the locals, ended up dominating and assimilating the local populations and the later caste system preserves to this day some differences in the amount of original Aryan ancestry even if ultimately mixing occurred at all levels.
There is essentially nothing false about this, the problem is trying to argue against ideas and theories that go far beyond this simple statement by attacking this unrelated concept.
People making wrong claims about the nature of the caste system, the chronology of the decline of IVC and the coming of the Indo-Aryan speakers etc. doesn't mean that we can pretend that this particular anecdote of human history is one free of violence or that it lays outside what we can call "invasion".
So yes, I can say “it’s not an invasion until proven otherwise” like many historians have been for years now. Because they simply weren’t invasions.
In the entire history of humanity we see so much violence in just about every facet of society, but in this event where an outside groups enters, dominates and ends up becoming a big demographic component of the newly mixed population, there was no violence or coercion? Did the locals somehow elect or voluntary choose the newcomers into power?
EDIT: Also the archaeological record shows that the de-urbanization of the last IVC cities was on its last legs by the time the Gandhara Grave Culture was formed. While I have no doubt the IVC cities fought amongst themselves via foreign mercenaries and militias towards the end of their Civilization, vast amounts of Indo-Aryans weren’t even in the continent at the time. So calling it an ‘Aryan Invasion‘ seems disingenuous when the IVC was mostly destroyed by the 4.2kya event causing irreparable damage to the monsoon cycle that watered their crops, don’t you think?
Why does prior internal decline of IVC disprove the idea of an invasion? Maybe you are using a very specific meaning of invasion, but honestly to me if there is violence and if there is a political takeover, it's simply an invasion. The fact you also think the Indo-Aryan settlers were mostly male is telling, doesn't it make them more likely to have been armed bands confronting established, albeit declining/collapsed, native societies instead of general migratory groups(like Slavs were north of the Danube) who simply encountered depopulated land?