So you're asking what entity has the authority to define what indoctrination is? Let's look at the definition of the word. Obviously, there are various organizational bodies that produce definitions for words so I'm just taking the standard Merriam-Webster definition here:
1
: to instruct especially in fundamentals or rudiments
2
: to imbue with a usually partisan or sectarian opinion, point of view, or principle
The reason why you see both teaching and imbuing associated with indoctrination is because both concepts apply. Now the moral authority behind indoctrination depends on what's indoctrinated and who it's coming from.
When GOD conveyed special revelation to humanity in the form of His Word, that was a form of indoctrination. In that case, the moral authority is positively present in the who and the what.
When a parent repeats what God has conveyed to their children, by extension the moral authority is present in the who and the what.
Governments (e.g. higher powers) are also ordained by God for the benefit of humanity within parameters that are always morally superseded by the de jure highest power (e.g. God). In whatever form the government may be, higher powers are always "under" or "below" God and never possess God's approval when it contradicts the good purposes for which God ordains government.
For example, God created the power of fire but the government is not within its moral authority to dictate that it's lawful to use fire to burn down the homes of your neighbors so you can steal their land from them. God created the power of sex but the government is not within its moral authority to dictate that it's lawful to engage in gross sexual immorality.
Because God respects human freewill, He has chosen to tolerate evil for a time. Look at what's happening in North Korea or occurred in Sodom and Gomorrah. But ultimately, God is going to restore and judge all things.
A good treatise on this subject is 'Romans 13' by Timothy Baldwin. You should read it.