The issue of dive watches without a timing bezel has been discussed often, here, and in other forums. It has generated animated exchanges...
Many believe, with good reason, that a watch without a timing bezel can not be called a dive watch because it is not useful to sports divers, and does not comply with ISO 6425 & DIN 8306 standards. As a sports diver, I think they are right.
Others indicate that dive watches without bezels have been used in the past, and are still recognized as dive watches by diving professionals. An excellent website on dive watches includes a few models (1, 2, 3) that are not equipped with bezels (with the author's reasonable "standard disclaimer" about their limited usefulness to divers...). Some watch manufacturers (Panerai, Anonimo) still make no-bezel watches that they call divers. Is that reasonable? Yes: they are right too.
There is a fundamental difference between sports diving with a scuba apparatus, and professional deep, "saturation" diving. Their requirements for timekeeping are different.
Sports (scuba) divers have a limited supply of air, and they might have to follow underwater decompression procedures, if they exceed their no-deco time limit for a certain depth. The longer & deeper a diver stays underwater, the more nitrogen penetrates & dissolves in their body tissues (incomplete tissue saturation ensues), and this nitrogen in solution might pop into bubbles when the diver ascends and the ambient pressure decreases, much as carbon dioxide in solution within a soft drink bubbles up when the bottle, or can, is opened.
These divers NEED to time their dive precisely, and their depth, in order to be able to follow decompression procedures, that also need to be timed accurately. Unless they have a modern dive computer, sports divers NEED a watch with a bezel to time their dive, and their deco times.
On the other hand, professional divers, if they dive deep and for prolonged periods of time, are said to dive "at saturation". They use special gas mixtures with lowered nitrogen, oxygen (normoxic = 21%) and sometimes lowered oxygen concentrations (hypoxic trimix, such as 16% O2, because oxygen becomes toxic at high pressures and causes seizures and other problems), with other gases, such as helium or hydrogen, replacing the nitrogen & oxygen in the inspired air. The gas is fed to them through compressors & tubes, rather than being carried in tanks. They dive "at saturation", meaning that because they stay for extended periods at depth, their body tissues become saturated with nitrogen. In fact, they really have no time limit to their dive, other than that caused by the cold and local conditions, and do their deco inside decompression chambers on the surface.
The requirement for accurate-to-the-minute timing is not present anymore, because in any case, their body tissues are saturated with nitrogen, and they will need to spend a lot of time (days) in decompression at the surface. They do need to have some idea of the time, and a Helium-venting valve is necessary.
(Helium, a very light gas present in the deco chamber, infiltrates the tightest joints of the watch. While the pressure in the chamber is lowered slowly, the pressure of Helium within the watch may remain high, and the watch crystal might pop out or break if the Helium within the watch is not vented).So, a timing bezel is not an absolute requirement for saturation divers. In fact, professional divers might not even be able to manipulate a timing bezel with their very thick gloves.
Thus, the Anonimo Professionale 2000, or Millemetri 1000 Hi-dive, with He-venting valve, really are to be considered dive watches and they might even actually be used by those Italian professional divers... for diving.
Other watches without a timing bezel, and without a He valve, (such as the Panerais) may be called dive watches, but the lack of a He valve creates a problem for saturation divers: the Helium may still be vented by unscrewing the crown, although this may allow humidity to enter the watch, and is really not optimal. These are not seriously designed for deep diving.
So, in conclusion: can a watch without a timing bezel properly be labeled a dive watch? Yes, if it was designed according to the specifications of deep, saturation diving. Is such a watch appropriate for sport diving? No, i don't think so.
There. I hope this is clear enough, that it helps clarify the subject, and that it will also decrease tensions in the forum! :-D