If you follow the way the private jet thing is done, it is structured as a gift to the government and not the president. It is perfectly legal and you won't be able to find any "proof" of corruption over it. This is how most corruption is done, in an underhanded manner, but everything by the book, with enough plausible deniability.
In many cases corruption is only known to the perpetrator, because it is a matter of intent. One can always proffer a different reason for what they are doing than what they actually intended and when those reasons later turn out to be false, you may never really know whether they acted in good faith in the first place.
So corruption largely comes down to perception end of the day. It is ultimately a matter of trust and when that trust is eroded, the perception of corruption grows. There's no smoke without fire. When we see smoke in a building, we do not go searching for proof of fire, we just gtfo because the risk is too much. We should do the same when we see red flags in people in powerful positions.
In many cases corruption is only known to the perpetrator, because it is a matter of intent. One can always proffer a different reason for what they are doing than what they actually intended and when those reasons later turn out to be false, you may never really know whether they acted in good faith in the first place.
So corruption largely comes down to perception end of the day. It is ultimately a matter of trust and when that trust is eroded, the perception of corruption grows. There's no smoke without fire. When we see smoke in a building, we do not go searching for proof of fire, we just gtfo because the risk is too much. We should do the same when we see red flags in people in powerful positions.