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I was under the impression that particle accelerators were pretty harmless, but some article said that they produce harmful radiation when you're in the tunnel. Given that the Internet... isn't always correct, is this true?

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Yes, off the top of my head I can think of two major sources of harmful radiation:

Synchrotron radiation: When charged particles are accelerated in a ring they emit EM synchrotron radiation. Depending on the frequency, this radiation can be dangerous.

Beam halo effects and internal beam interactions: Beam halos, are particles in the accelerating bunch which are electromagnetically repelled from the beam centre. Particles in the beam halo are often lost to the walls of the beam-pipe. These, together with interactions in the beam can lead to various high-energy particles being produced.

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To extend jk88's answer, I'd like to say that in addition to the "prompt" radiation there is the possibility of activating material near the beamline.

Prompt effects are what jk88 is talking about and they go away when the beam shuts off, except that any neutrons generated hang about for a short time.

But the prompt effects can activate material near the beamline. That is, it can make some of the material nearby radioactive in and of itself. This is a fairly minor effect in most of the tunnel, but near targets and beam dumps it can be much more significant.

The biggest danger from activated material arises from the activation of dust or other mobile material , which can stick to you shoes, clothes or skin and be carried away with you. In the worst case it can even be ingested.

Considerable effort goes into preventing the activation of mobile material, detecting and cleaning it up when it does happen, and preventing people for coming into contact with it and from leaving the enclosure unscreened if they do.

It is, however, rare for activated material to pose an immediate acute threat like the radiation environment near a running high power accelerator can.

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I'm sitting at a conference at a Japenese accelerator, listening to the director explaining what went wrong during the recent accident that release radiation in the athmosphere and in a room with some workers inside, so I guess the answer is yes.

EDIT : my answer was quite sarcastic, but it was to show that it is not only a theoretical danger, it happens sometimes

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