I think you hit the nail on the head when you said DC. Direct Current is funneling electricity in one direction, where AC is a bit wacky. For one thing, with AC you not only have Voltage and Amperage to think about, but also Frequency.

Arbitrarily, AC cycles at 60hz throughout the US but just because we're consistent doesn't make it natural. One great example I saw was on Mythbusters, Jamie & Adam were trying to use electricity + acid to eat through the bars on a jail cell. Adam, not thinking the science through as usual, was using AC and couldn't seem to get anywhere. Jamie used a battery and it ate right through the bars no problem (after about a month or something).

The difference was that the direct current, combined with the acid, moved the molecules of metal from the bar always in the same direction, while the AC power kept taking molecules of metal off the bar, and then reversing direction to put them right back on the bar relatively near where they came off — misshaping the bar slightly, but not making it any thinner.

Essentially, DC is the natural order of things. Tons of electronic devices have converters that allow them to plug into an electrical outlet, but then convert the current to DC so the device can function. Many devices also run on AC by design, but ultimately the only reason AC became mainstream is because it needs half as many wires for infrastructure and therefore the enormously expensive task of running powerlines to absolutely everywhere is literally 50% off.

Historically, this is Nicola Tesla's final revenge on Thomas Edison — not that it did Tesla any good. Ultimately, Tesla's inventions were largely impractical (even when theoretically genius) and Edison always got better contracts and more public acclaim, but when it came to pushing DC power the price difference was just too much for Edison to overcome and Tesla's (and Westinghouse's) long-touted Alternating Current won out as the design electric companies would follow.

Edison's primary (and still excellent) selling point was how dangerous AC was. Obviously, we all know that a downed power line will kill you dead in a heartbeat (or quite literally in between heartbeats) but also fear is a powerful motivator in general, even when less justified. Edison went so far as to publicly electrocute an elephant (killing it) in order to scare people away from AC electricity. You can watch the sad spectacle here: http://www.youtube.com/watch?v=RkBU3aYsf0Q

Anyway, sorry for the tangent but it's interesting history. The relevant point here is that Direct Current is simple, natural, safe, and easier to utilize than AC. Most people don't realize that light bulbs (for instance) turn themselves on and off 120 times a second (in the US), visible only in slow-motion video. Every time the current reverses, the electrons have to flow the other way. Due to the complexities of AC power, I think it's plausible that if something existed in nature which could draw upon electrical energy, it would probably would greatly prefer some form of DC power and probably wouldn't know what to do with AC.

That being said, I still think the most likely explanation is either they're not properly charging their equipment or else the batteries should be replaced. Notice how when something happens with a crew member (camera or audio guy) they never hesitate to tell us about it, but I've never once heard about one of their camera guy's batteries dying — probably because they are professionals that remember to properly charge their equipment.

Of course, this is one of the standard philosophical objections to ghostly phenomena in general. If ghosts are supposed to be completely non-physical– "A person without a body"– then how can they have any effect on the physical world at all? How can they drain batteries, cause cold spots, make sounds, move chairs, or interfere with your digital recorder? It takes energy to do all of these things, and energy is part of the physical world.