What size tank were you diving? 25 minutes on 1100 lb in an AL80 at the entrance to Devils Throat is pretty good! Of coarse, 25 minutes below the entrance of DT is pretty good too. Those guys must have been pretty deep into deco unless they were diving 32% beyond its 1.4PP limit. My wife and I have opted out at the DT entrance twice. Once because we were already too close to deco and once because we were on 32% and I didn't want to test it at 130. Both time we followed the bubbles and came out over the exiting divers. Didn't take 25 minutes though!
A reputable dive shop gave you a 32% Nitrox bottle and took you to the Devil's throat? The MOD at 32% is only 107' at 1.4 PO2 on my Cobra; so this is so unwise i almost think you must be mistaken and could be a recipe for disaster. You were very smart not to attempt this.
I've done this dive twice, with experienced divers only, and I am TDI Cavern certified. It is far from the best dive on the island, but remains popular and is considered iconic, which is unfortunate. It can be done safely without deco obligation on an AL80, even on my Suunto Cobra, as the swim-throughs get progressively deeper and you are not at 130' for an extended period. Nearly all shops use AL 80's for this dive unless otherwise requested, with a few notable exceptions. You may get very close or go into a 4 or 6 minute deco on a Suunto that will evaporate as you slowly ascend, leaving you with just a safety stop. I personally do not consider it to be a full cave dive, and I do not recall any sections that are completely dark, although some are pretty dim. I do consider it to be a cavern dive, and while overhead training may not be a requirement for this dive maybe it should be and it is certainly helpful. I always carry a light and DSMB, along with a storm whistle (that thing HURTS if you blow it too hard without dipping your ears in the water) and signal mirror everywhere, but many of these are especially important for drift diving in Cozumel or similar drift diving locations with significant current. This was taught to me in OW, but I had a particularly attentive instructor, and I had made it clear we were planning our first dive trip to Cozumel. We took several practice dives and completed AOW before that first trip due to the nature of the dives we would be making. I did not do (and would not have attempted even if offered) Devils throat on that trip - not until a trip a few years and about 150 dives later. I will say that the dive shop I use will not bring anyone there with whom they do not have extensive experience, and make both that and the deep, dark, and overhead nature of the dive extremely clear up front to anyone who requests it. Needless to say, NITROX is not on the menu. To answer the OP's basic question, yes, I think recreational divers can be brought here, but only with the specific conditions of the dive clearly known up front and only if they are properly equipped and experienced.
That said, based upon the OP's report and responses, he did pretty well to manage a difficult situation, and has realized he needs to modify his kit for drift dives. As others have said, an DSMB or SMB at minimum is required and it does not hurt to carry a light on all dives (I use one at least a few times on most). Adding surface signalling options is a must for all drift dive locations, most especially deep sites like Devil's Throat or even more so for the more remote, less frequented northern fast current sites in Cozumel like Barracuda. If you can't signal your boat there you have a slow one way ticket to Cuba.
