Some of the proverbs are instructional while others are observational. In no way is the Bible endorsing giving bribes to subvert justice - but God, the One who has inspired the Scriptures, is also not blind to the observation that bribes do exist and they are used to turn away anger and wrath. In understanding this proverb we do need to focus on the fact that what is being said here deals with the issue of those who are angry and filled with wrath toward another. This is not a proverb dealing with wanting to pervert justice - it is about dealing with those who come to a court situation and who are very angry. It is written with truth that will help those who are wanting to lessen that anger before they get to court. So what is this proverb telling us - and what observation is it giving to us?
When facing anger and wrath from someone - it is helpful in subduing it to offer a gift or a bribe. Bribes do exist - and unfortunately the rich use them to subvert justice. When a situation arises when someone is very angry and they are considering acting in the wrath of the moment - a bribe will help tone down the anger. Is this righteous? Most likely in the case of the bribe it is not. Is it effective in the world? Unfortunately it probably is. But there is another way of looking at the statement that a gift in secret subdues anger.
Those who know of court proceedings know that many cases are "settled" out of court. What is often done is that lawyers offer a "settlement" to make a case or a person's anger go away. The injured person is willing to have a sum of money - a gift given in secret if you will - subdue their anger and move them to drop the suit in court. These settlements usually involve fairly large amounts of money. They are meant to pacify the anger of the one who is bringing the suit or threatening to do so. When this gift is given in secret - the case goes away. For those who know that they are in trouble and guilty, yet do not want a court or a jury deciding the award in the case, a settlement may save them millions of dollars. For the person injured or wronged, it saves them the difficulty of the court case itself - and the risk of getting nothing. In the end, though everyone may not be completely thrilled, it does subdue the anger and settle the dispute.
Remember though, this is a proverb that is observatory. It is observing what happens in life - not dictating what should happen. In this regard it is good to know these things - and to know that God knows too. God knows that often these things will happen - but one thing to remember is that they will never happen at His bar of justice. When we stand before God, there is no amount of money or works that will speak for us subduing His wrath. The only thing that speaks in that day is the blood of Jesus Christ shed to pay for our sins in full. There will be no bribes or gifts passed under the table. God Himself has made the way of payment for sin - but know this - it is the ONLY payment accepted.