Cryptograhically random unique strings

Question

In this answer, the below code was posted for creating unique random alphanumeric strings. Could someone clarify for me how exactly they are ensured to be unique in this cod

Answer 1

Using strictly alphanumeric characters restricts the pool you draw from to 62. Using the complete printable character set(ASCII 32-126) increases your pool to 94, decreasing the likelihood of collision and eliminating creating the pool separately.