They're supposed to be.

At an industry gathering a few years back, one of my cohorts at another airline related the story of one of his transcon flights with an in-flight medical situation. As was the usual procedure, the flight initiated a VHF radio call via ARINC, who called the contracted medical service, as well as the flight's dispatcher, and patched everyone in together. They were enroute AAA-BBB, and after discussion the Doc ended up recommending a diversion to CCC (closest airport) which was roughly around the mid-point of the flight. The captain immediately acknowledged it and said that they were now heading to CCC. The dispatcher then chimed in that the weather at CCC was not only below landing minimums but also out of crosswind limits, and further, that he was instead diverting the flight to DDD (next closest airport, albeit in a different direction) that had acceptable weather conditions. The flight time to DDD was about 15 minutes longer than having gone to CCC, but it was obviously the safer thing to do, not just for the ill pax, but the other 199 pax also on the aircraft.

The captain would have eventually checked the CCC weather via ATIS during the descent, but the point is that should have been done before the divert decision, and is also precisely why the dispatcher is there in the first place--to backstop and otherwise cross-check critical decisions. It's the same rationale as nuke subs having two folks with missile launch keys--it precludes rogue behavior, either inadvertent or intentional.

As a general rule, pilots do a great job of looking out for threats to the "bubble" around their individual aircraft, but commonly fail to adequately consider larger-scale systemic issues and the "Big Picture." Nor can they in many cases, since the dispatcher has many more info sources at their workstation than a crew does onboard the aircraft. The role of the dispatcher isn't to in any way usurp PIC authority (as many of them seem to feel) but supplement it. Two heads are better than one...