The continuum you describe is absurd. Removing rules for noncombat, nonadventuring skills, and replacing them with ad libbing and DM/player consensus, doesn't make a game less like a LARP.It's not an equivalent, but where a minis wargame is one end of a continuum and LARPing is the other, 4e slides you toward the wargame from 3e's ever-so-slightly-more character/world focused stance, because its rules for dealing with things that aren't putting pointy objects into squishy things that scream are more lacking than 3e's were (and 3e's were hardly a bastion of good resolution to begin with, but they were better than a broken Skill Challenge system).
That, ultimately, is the kernel of truth in these "4e feels more like a boardgame"-style observations. They aren't all just gut-reaction 4e-bashing.