There is some truth to that and passages such as Job 1:11-12 and 1 Cor. 5:5 makes a strong case for it. But I would not say any of that without qualification. My book and other writings give more detail about how all of this works in Scripture. One example is the fact that people actually start out forsaking God before He forsakes them (Deut. 31:16-18; 2 Chronicles 15:2; 24:20). We actually leave God's umbrella of protection.
Numerous Scriptures show God pleading with the Israelites to return to Him so that He would not have to remove His protection from them. But when they constantly reject Him then He is left with no other choice but to leave because He has been pushed away. However, when they repent and return to Him after suffering God jumps right back into action and rescues them from their oppressors.
That is a good observation because many do think that I teach a passive judgment of God which is not completely true. God is actively involved but not in the way that you might be implying that I teach but especially others who traditionally teach about God launching fireballs to kill those who angered Him.
God is active, as I stated above, in continually pleading with His people to return to Him so that He would not have to remove His protection from them. When they choose their idolatry over Him then He finally says:
Deuteronomy 32:37-38
37 And he shall say, Where are their gods, their rock in whom they trusted,
38 Which did eat the fat of their sacrifices, and drank the wine of their drink offerings? let them rise up and help you, and be your protection.
In other words, you want to forsake God and worship false gods, then depend on them to protect you. It is unreasonable for God to keep protecting those who prefer to continue sinning. The fact that He even remains protecting them for some length of time when they fall into sin shows His great mercy.
That is how God is vindicated in all of this.