No. No, we do not see it that way.
It's also meaningless because the whole concept is flawed. Crimes do not occur above the sovereign nation state level. "War crimes" is a convenient excuse for the winner of a conflict to execute the leaders of the losing side. It's victor's justice.
(It's not really ex post facto anyway - you simply apply the existing (1945) standards for what was considered a war crime, and find that the bombings fit the bill [1]. That seems to me the best way to do it - what would you prefer? That no one had used an atomic bomb before, need not exclude the possibility of the first such use of one being a war crime.)
That said, I mostly agree with your take on war crimes in practice, if not in principle. But if the allies had lost the war the bombings would have been considered a war crime by the victors, without a doubt. In that sense it is appropriate to call it a war crime. Again, it was a war crime in a war replete with them, and it was not the worst of them either: it was certainly no Holocaust, and I don't think the two bombings taken together even rise to the level of one Rape of Nanjing, either - but it was a war crime and yes, that is the popular opinion of it globally.
Try to keep in mind that I'm mainly defending the original statement "we understand that it was horrible war crimes". That is an accurate statement, even if you have grounds to think that people are wrong to see it that way.
[1] https://en.wikipedia.org/wiki/Debate_over_the_atomic_bombing...
Evidence? Whether allied strategic bombing of Germany/Japan was a "war crime" is partly a legal / technical question:
https://en.wikipedia.org/wiki/War_crime#Definition
In regard to the strategic bombing during World War II, it should be noticed that at the time, there was no international treaty or instrument protecting a civilian population specifically from attack by aircraft,[34] therefore the aerial attacks on civilians were not officially war crimes. Because of this, the Allies at the trials in Nuremberg and Tokyo never prosecuted the Germans, including Luftwaffe commander-in-chief Hermann Göring, for the bombing raids on Warsaw, Rotterdam, and British cities during the Blitz as well as the indiscriminate attacks on Allied cities with V-1 flying bombs and V-2 rockets nor the Japanese for the aerial attacks on crowded Chinese cities.[35]