In my experience with my horses, it is true. No, it does not have a vise-like clamp around the horse's face, but it doesn't have the instant release of pressure that a side-pull has. Both horses I used with them became irritable, and were fine when I went back to a cheap side-pull.
It may be different with a different brand or material. The ones I used were made out of marine rope, and maybe biothane or leather gives a faster relief. It could also be that a difference in the horse's face or some other variable gave different results.
I think the material definitely has a big part in it, and also the inability with any kind of rope halter to really fit it snugly to your horse's head without it slipping. What also matters is the default tightness of your reins. I can't imagine having no release if you normally ride with your reins in an arc or just very light contact, unless the material is too rough to slide back through the ring smoothly, or somehow moves over your horse's head so it can't move back. I'm not even talking about a horse's responses to it (you're right, those are different), just he biomechanics of the bridle itself.
The size of the head and nose and the size bridle might also be an issue.. It's easy to imagine that the less bend in the strap you're pulling on, the easier the release will come, so logically if the rings on your bridle are more towards the chin, your release will be better.
Thing is, I have tried riding my horse in a sidepull (the noseband of my Dr. Cook type bridle without the cheek straps with reins attached to the rings on the noseband) and the problem is that one-rein half halts just don't seem to come through to where I want them. Also my horse has the tendency to hang on the reins, and the only result of hanging on a bridle with running straps is that he will it tighter himself. Since we've been using the Nurtural he has completely stopped dropping his head's weight into my hands, until I tried it with that sidepull.
Are you sure it's the release that made your horse's agitated, and not the multitude of signals a cross-over bridle can give? Pressure on the nose, on the cheek and on the poll for just one cue can be confusing for some horses, and some also just don't like the sensation of something hugging their head.