Was Roman expansion & casus belli as just as they claimed?

I find it a bit too convenient and Rome's greatest extent too large to be believable . . . Why do we believe it then?

Actually, we don't.

Historians recognise that the Romans liked to claim their wars were "just and righteous". Equally, however, it is recognised that this was mostly bunk. In fact, modern scholars argue the Romans increasingly perverted the idea of "just wars" in order to justify their aggressive expansionism:

From the 2nd century BC on wars, Romans thought of all their allies as subservient, what we would call 'client states', and any people who had had diplomatic dealings with Rome could be thought to fall into this category. Failure by an ally to comply with the wishes of Rome constituted a breach of faith, and thus Roman 'revenge' would be a just war. It did not end there. Any injury to Rome, not only an attack on it or its allies, could call for revenge. A hostile attitude, or even the mere existence of a foreign power, could be considered a threat to the salus of Rome, and thus Roman aggression could be a just war.

_{Sidebottom, Harry. Ancient Warfare. Oxford University Press, 2004.}

In other words, when the Romans claim to be the "victims", it doesn't mean they were actually victimised in any sense of the word that you'd recognise today.

it seems so strange that they always were given some real reason to conquer some place instead of just being like "We hear there's gold in this place, so we will invade it".

From a historical perspective, this is not that strange or unusual at all. It's a recurring, albeit not universal, feature throughout history for combatants in a war to claim they are on the side of the righteous. As long as greed isn't considered a virtue (and it usually wasn't), people throughout the ages have been reluctant to admit that's their true motive for war.

This isn't just a Roman or Western thing either. For example, his biography in the Book of Han records an advice the First Han Emperor once received:

臣聞『順德者昌，逆德者亡』，『兵出無名，事故不成』

Your majesty, I hear that conforming with morality leads to prosperity; contradicting ethics leads to ruin. Going to war without a just cause will only result in failure.

Everyone is the hero of their own story, and the Romans were simply no exception.

What I imagine would be normal "imperial" behaviour is like what Hungary tried to do many a time against Bosnia; nag the pope that they're heretics and then try to conquer the land because you want to have it

This really isn't any different from the Roman examples. The Hungarians may have simply wanted the land, but that wasn't their stated excuse to go to war. As you yourself hinted in this example ("nag the pope that they're heretics"), the Hungarian excuse was that Bosnia was infested with heresy.

Fighting heretics or infidels was considered very much a "just war" by Medieval Christians.

Is there proof that all of these explanations, backgrounds or chronologies we have are at very least very likely to be spun in the favor of Rome

All of them? No. Certainly Rome did fight some wars in self-defense.

However, as the above quote demonstrates, just because the Romans claim to be the victims doesn't mean their reasoning wasn't obvious self-serving excuses. Take for instance the Third Punic War, where Rome all but forced Carthage into war with an unending series of unjust, oppressive demands, and yet deigned to call themselves the victims. None other than Polybius provides ample proof ot the Roman injustice in this regard, reported that some observers:

took the opposite view, saying that far from maintaining the principles by which they had won their supremacy, [the Romans] were little by little deserting it for a lust of domination like that of Athens and Sparta . . . For the Carthaginians had been guilty of no immediate offence to Rome, but the Romans had treated them with irremediable severity, although they had accepted all their conditions and consented to obey all their orders.

Others [say] in the present case, throughout the whole of their proceedings in regard to Carthage, [the Romans] had used deceit and fraud, offering certain things one at a time and keeping others secret, until they cut off every hope the city had of help from her allies. This, they said, savoured more of a despot's intrigue than of the principles of a civilized state such as Rome, and could only be justly described as something very like impiety and treachery.

_{Histories 36. 9.}