No, not necessarily. It's standard practice to pick a p-value significance cut-off (0.05), but report the smallest such standard cut-off that any particular value meets. So "p < 0.001" is reported for values that meet that threshold. Anything over the cut-off is just not reported as significant.
That seems dishonest to me. They're saying that some results are more significant after the fact. Is there any mathematical justification for why this is OK?
