I was just going to comment in SF1's fanpost, but it started getting long. To sum up, here is the assertion:

Rays simply aren’t good hitters in terms of batting average, so throw strikes until they prove they can hit with authority. If that changes we’ll begin to see BB go up, because pitchers will be more careful

This has been the dominant narrative on Rays broadcasts as a team-wide phenomenon, but it's probably more useful to go player by player. If it's true, the fact that opposing pitchers are throwing more strikes should show up in the plate discipline stats (I'm using www.fangraphs.com).

Damon:
Career  BB% - 9.3, this year 2.6.
Career Zone% - 51.9, This year 48.3
Verdict: False - pitchers have so far thrown him less strikes than they usually do. He's not walking because he's swung at more pitches, both in (65.2% career, 75.4% this year) and out (20.6%, 31.6% this year) of the zone than he normally does.

Reid Brignac (SSS Warning):
Career  BB% - 5.4, this year 3.8.
Career Zone% - 44.0, This year 51.5

Verdict: Plausible, but weird - Brignac has a big, uppercut swing with holes in it, and he's a hacker. He was never one to take a walk. So far, pitchers are throwing him more strikes, he's swinging at very slightly more pitches, and making significantly more contact overall, but especially in the zone (91.7%!!!!!!!). This should be a good thing, right? Shouldn't this mean that pitchers' approach to him is minimizing his weakness? Well, he's hitting for no power. Doesn't make a whole lot of sense to me, and I hope it doesn't continue.

Kelly Shoppach:
Career  BB% - 8.6, this year 2.8.
Career Zone% - 49.6, This year 45.5
Verdict: False - Shoppach is swinging at way more pitches over all, both in (83.3%, 71.2% this year) and out (28.0 career, 47.2% this year). Pitchers are throwing him less in the zone and he's swinging at more. He must stop, and he will. This is an extreme small sample size.

Sam Fuld:
Such a small sample size, nothing to look at here. Suffice it to say that he's posted a good walk rate in the past and in the minors, but right now he's busy enjoying a wOBA over .400.

Sean Rodriguez:
Career  BB% - 6.7 (but good in the minors), this year 9.8.
Career Zone% - 51.0, This year 42.7
Verdict: False - He's also swinging at a bit less outside of the zone, which is good. He's always struck me as a guy with a good approach but only an average eye. Maybe last year was just an aberration and he's better than that.

John Jaso:
Career  BB% - 13.3, this year 4.5.
Career Zone% - 44.2, This year 48.2
Verdict: True - He's swinging at slightly more outside (18.5% career, 19.3% this year) and a bit more inside (53.6% career, 57.3% career). Still, this seems to me like a case of unlucky grouping. Those numbers are still excellent, in regards to the rest of major league players, and should produce walks. The real story is he's getting BABIP'd real bad (.167). The surprising nature of his performance last year makes it easy to fear that the sky is falling, but I really don't think that it is. Too much of what made him good is still there.

BJ Upton is walking in line with his career rate. He's also seeing fewer pitches in the zone.

Ben Zobrist:
Career  BB% - 12.2, this year 9.2.
Career Zone% - 47.5, This year 48.5
Verdict: False - Zorilla is making less contact (83.3% career, 73.1% this year), especially out of the zone. He's driving the ball, though, and his swing doesn't look any different to my unskilled eye, so I'm not too worried.

Matt Joyce:
Career  BB% - 12.4, this year 8.8.
Career Zone% - 45.5, This year 51.1
Verdict: True - But he has a LD% nearly double his career rate and a HR/FB of 0. The former means that pitchers aren't winning by challenging him (therefore they won't continue to do so) and the latter is just plain silly and won't continue.

Dan Johnson:
Career  BB% - 12.9, this year 4.6.
Career Zone% - 50.5, This year 52.7
Verdict: Doubtful - That's a pretty marginal Zone% upgrade. He's swinging at more pitches overall, though (37.5% career, 47.4 this year). That's just not the DanJo we saw last year, or any one in Oakland (and I must assume Japan) saw either. He really just needs to chill out. My guess is he goes on a major walking spree as soon as Howell comes of the DL.

Really, this narrative only applies to Jaso and Joyce. And Joyce always and obviously had the ability to punish a careless pitch, so I doubt opposing pitchers are actually trying to pound the zone on him. It's a good story, but it's just not true.