Even before Woodson's comments, it would have been reasonable to question Anthony's playing time allocation as of late. Aside from playing the more grueling power forward spot—where he has played 54% of his minutes this season, up from just 19% last season, according to 82games.com—Anthony has logged considerably more minutes in recent months.
He averaged about 35 minutes over the Knicks' first 10 games, when they were blowing opponents out, but has averaged 40 minutes since Christmas. Not coincidentally, Anthony's two worst shooting months by far were January (42%) and February (40.6%).
You could definitely criticize Woodson for not finding more rest for his star player, but it's also worth noting that the team has played short-handed a good portion of the season, particularly at the power forward spot that Melo routinely plays. It had to be a concern that all these minutes could wear him down, but in the coach's defense you're also trying to win these games and I can see the temptation to say, "Hmm, I think I'll just Melo back in. That seemed to be working."
That's not to completely absolve the coach, but I also don't think it's a straight line from he's playing five or so more minutes a game than you'd like and oh, his knee is hurting, that's 100% the cause. It very well may have come about either way.
To that point, the early word is that Kurt Thomas will be starting in his place, so perhaps we can see the hesitation to reducing Anthony's minutes, even if I don't really get that particular strategy. This potential James White/Kurt Thomas pairing sounds me as particularly bizarre, "Hey, let's play two of our worst players for the first couple minutes and then not at all after that." I don't really get it.