The Greek phrase translated to this actually indicates that nothing happens to any of us outside of God's will. The word ἄνευ means without "one's will or intervention" according to the lexicon.
In other words, everything that takes place, takes place because the Supreme Being allows that to happen. He is in complete control and nothing happens outside of His will.
This is a critical lesson for Jesus' students and all of us. But does it assume there is no freedom of choice? That all things are per-arranged?
Don't be ridiculous. The Supreme Being gives each of us choices. Ultimately, we each have the choice to love Him or not. This is because love requires choice.
And the Supreme Being also allows us to make other choices - each typically stemming from this ultimate choice.
This is the design of both the spiritual realm and the physical world. But the physical world is especially a place of choice: It is that place where are constantly being presented with choices.
But it is also a world where there are consequences for every choice we make. This is because the physical world is also a place of learning.
We might compare it to a child's bedroom. Everything in the child's bedroom was put in there by the parents. They also own the house. But this doesn't remove the freedom of the child from choosing which toy to play with. It also does not restrict the child from choosing to obey or rebel against his parents. The child can choose to rebel against the parents and rip everything up if he wants. Or he might just be a good boy and do what he is told.
These choices are up to the child. The parents cannot take the child's freedom of choice away. They might own the house and control what is in the house. But the child still has the freedom of choice within that house.
In the same way, the Supreme Being gives us certain freedoms to make choices. These are our choices to make. This doesn't mean He gives up control. He grants the freedom because this is necessary in order to enjoy exchanging love.
If we choose to partake in our natural loving relationship with the Supreme Being this is pleasing to the Supreme Being. If we rebel against Him and choose to forget Him, it is not pleasing to Him. Why not?
Because the Supreme Being enjoys loving exchanges. The Supreme Being enjoys exchanging love just as we do. This is why Jesus' most important instruction was:
" 'Love the Lord your God with all your heart and with all your soul and with all your mind.' This is the first and greatest commandment." (Matt. 22:37-38)
(For a translation of Jesus' statements from the Book of Matthew without institutional sectarian influence, see the Gospels of Jesus - translated from the original Greek texts.)