I don't know if that's true. They only had 3 draft picks in 2009 and 4 in 2010. Lots of wheeling and dealing going on there, but 2009 was noteworthy because of the Sanchez trade, and they also traded a few picks to go up for Shonn Greene in the third. I think the Jets at the time felt like their roster was ready for a serious run (and it turned out to be true). 2011 they started a run on DL in the first, but Mo was necessary because they lost Shaun Ellis. Coples was probably the wrong choice for them in 2012, but Richardson was a great choice in a year where they got the extra pick for Revis and drafted a guy to theoretically replace him. After that they went safety and tight end so I think that makes three DL/LB in six years. They did take a WR once - Stephen Hill, terrible choice - but drafting more skill position players may not have helped because of their main issue:
The main issue for them was QB. Sanchez wasn't the same after the 2010 season. No confidence, no leadership, poor performance, etc. They failed to address that issue and it all fell apart.