The three-digit numbers are represented by $( ABC )$, where $( A )$, $( B )$, and $( C )$ are non-zero, distinct digits. Using these three digits, we can form $( 3 \times 2 \times 1 = 6 )$ unique three-digit numbers.

To find the sum $( x )$ of these 6 numbers, we aim to locate two values of $( x )$ closest to 1000: one just below it (which would be the largest 3-digit value for $( x )$) and one just above it (which would be the smallest 4-digit value for $( x )$).

We start by testing the smallest possible digits, 1, 2, and 3: Calculating $( x = 123 + 132 + 213 + 231 + 312 + 321 = 1332 )$.

This result, 1332, is the lowest possible value of $( x )$, verifying that Statement 1 is correct. However, because 1332 is already a 4-digit number, there is no way to achieve a 3-digit result for $( x )$ using non-zero digits. Therefore, Statement 2 is incorrect.