Not true. The name of the tree is tree of knowing good and bad, and it clearly states that once eaten they were only than able to differentiate right from wrong (or good and bad).
It was not necessary to know evil in a perfect and sinless world. By eating the fruit they unleashed evil not only into the world but also into themselves. Ever since then people have been born with an inherent sin nature.
Jeremiah 17:9
[9]The heart is deceitful above all things, and desperately wicked: who can know it?
Psalms 51:5
[5]Behold, I was shapen in iniquity.
This changed something inside of them and it was not good.
It is only necessary to study for a task you intend to perform. A carpenter does not need to learn how to knit. It is not necessary to learn evil unless you intend to do evil.
Romans 16:19
[19]...I would have you wise unto that which is good, and simple concerning evil.
Proverbs 9:10
[10]The fear of the LORD is the beginning of wisdom: and the knowledge of the holy is understanding.
It is not necessary to know a lie in order to know truth.
God is truth.
John 14:6
[6]Jesus saith unto him, I am the way, the truth, and the life: no man cometh unto the Father, but by me.
Psalms 31:5
[5]...Thou hast redeemed me, O LORD God of truth.
John 16:13
[13]Howbeit when he, the Spirit of truth, is come, he will guide you into all truth...
God's word is truth.
John 17:17
[17]Sanctify them through thy truth: thy word is truth.
John 8:31-32
[31]Then said Jesus to those Jews which believed on him, If ye continue in my word, then are ye my disciples indeed;
[32]And ye shall know the truth, and the truth shall make you free.
God is the source of truth.
The tree of the knowledge of good and evil was only made that man might have free will. It was the ability to choose it that gave him his free will, not the action of choosing it which was the wrong choice.