I saw this amusing problem on facebook, and figured some mathematical logic could be applied to it.
I think the answer is 042. According to lines 4 and 5, 0 must be right but cannot be put in block 3. According to line 3, 0 also cannot be put in block 2, which means 0 belongs to block 1. According to line 1 and the previous conclusion that only 0 belongs in block 1, that means 6 is both wrong and out of place. As 8 is wrong by line 4, that means only 2 is correct and in place. At this point only 1 or 4 can be correct from line 2. 4 is in the wrong place, though this doesn't necessarily mean it's correct. Looking at 1, if we assume its right and in the wrong place - we'd have a contradiction because only block 2 is left which would make it also be correctly placed, therefore only 4 can be true.
Hence, 042.
Am I correct? Apparently the original poster is saying I'm wrong, but refuses to explain why.
Your suggested answer of $042$ satisfies all of the conditions in the $5$ stated clues. As such, it is at least one correct answer.
However, one important thing to note, though, is the implicit assumption anything not explicitly stated in the clues is excluded. For example, the first one says
It doesn't explicitly say anything about the behavior of the other $2$ digits, although the assumption is they are both wrong. In this case, though, clue $4$ explicitly states $8$ is not a correct digit, so it's just a matter of whether or not $6$ is a valid digit. Also, note the statement could mean there is just one digit which is right and in the correct place, so there could be another digit which is right but is in the wrong place.
Note if you allow the statement to not necessarily mean anything about the other $2$ digits, as well as clue $3$ not stating explicitly about the third digit, then note $062$ would then also meet the conditions of the other $3$ clues. Perhaps this is the answer the original poster is thinking of, or maybe another one obtained from this more permissive interpretation of the clues (I don't believe there is, but I haven't done any exhaustive check to make absolutely sure).
Regardless, if this is the case, I believe this is a poorly worded question, so even if you allow multiple answers, your answer should be considered to be the "best" one. Also, it's not appropriate for the original poster to say you're wrong, as your result is correct. Instead, they could perhaps state there's more than one answer and they have a different one from you.