Well, my uneducated opinion is that the water is owned by the commonwealth, and the DEP does have the authority to permit or deny water withdrawal permits.
Of course, the trucks cannot trespass on private land without landowner permission. And in the case of non-navigable waterways, the streambed and streambanks are private land. So they'd have to get it from a right of way, park, national forest, state forest, etc., somewhere where the government owns the streambed. In navigable waterways, everything up to the high water mark is public, including the streambed. So there, they just have to access the water legally, but once to the streambank they can go up or down.
All in all, I think this is a poorly thought out defense by the Allegheny Defense Project. They are merely trying to oppose the gas industry anywhere they see a chance, and I understand that motive (may not agree, but understand). But I think they're endangering themselves here. If they actually succeeded in this objection, then you have taken the right to monitor water withdrawals away from the DEP or any central authority whatsoever, and made it a free for all among landowners looking to get money. I don't know whether the DEP is currently being stringent enough on the withdrawals as far as minimum flow rates and such. But at least, if it becomes a major problem, they have the ability to get more stringent. You don't want to lose that card.