EXACTLY what is a "luxury" pick?
Understanding that you weren't asking my personal opinion, I believe that when you repeatedly are drafting years ahead with younger players in the pipeline, and also have the high majority of positions and starters already filled ahead of time, one can reasonably argue that we were certainly in a position of luxury for some of our picks this year. If you take the excellent depth of the entire draft into account, this means that Belichick was able to roll the dice a bit more due to the value that could be had later in the process.
The 2014 period of free agency (Revis, Browner, LaFell) was also quite helpful in addressing any holes that we had just as well, since there is a 2 pronged approach in the spring via the draft + FA. We were relatively aggressive in that regard with some bigger splashes than in most "normal" years.
If you want to even take it one step further, no one (and I mean--no one) was expecting a 4th round pick as a compensatory selection either. All of the experts such as Miguel and Jason were expecting a late round choice that occurred in the 6th round or so, as this was the highest compensatory pick that we've had in awhile. The addition of that pick allowed us to have 5 selections in the top 140 players of arguably the deepest draft in at least ten years, if not more.
And just to wrap it up---we have enormously talented players who are coming back from injury that did not contribute to the 2013 team which includes: Mayo, Kelly, Wilfork, Gronkowski, Vollmer, and Armstead. Again...not too many positions or starters that weren't already penciled in ahead of time, especially after the period of free agency.
I think a much more appropriate question would be "
how didn't we sit in a position of luxury" as it pertained to the 2014 draft this spring?