The internet is filled with conflicting information because a lot of it applies to different scenarios.
Firstly, there's a paired device and a connected device and then an actively communicating device. Your links above confuse these and no distinction, but there is a difference in functionality. A device can be paired, but not connected. Similarly, it can be connected but not transmitting. Think of a paired device as a saved wireless network that you're not connected to.
Then there are host devices and client devices. This is a generalization, but consider PCs, mobile phones, and tablets (and consoles) to be hosts, and headsets, controllers, mice, keyboards, etc. to be clients.
Then there's profiles, a profile indicating a type of connection (e.g. audio, HID, etc.)
With that in mind, the following apply:
In general, host devices support up to 7 simultaneously connected devices and a practically unlimited number of paired. Host devices are like a wireless router - you can connect many different devices at a time.
Client devices typically support a limited number of pairings, anywhere between 1 and 5, and only one single connection. They act like a wireless client - you can save many different networks but only connect to one at a time.
Some profiles only support one connection at a time on some devices - for example, some Bluetooth speakers can only connect to one computer at a time. A phone for example usually can only connect to one HSP (headset) at a time but can connect multiple HIDs (keyboards, mice, etc.).
Also, to explain/clarify some of your links/references:
- All Bluetooth adapters can support 7 devices, period.
Mostly true - the standards only allow up to seven simultaneous connections on a normal device. But you can pair any number of devices.
- You can hook up 7 devices, but only if they're all different types of
False, but in some scenarios, you cannot simultaneously use two devices with the same Bluetooth profile. This generally applies to audio devices only (i.e. headsets) which may be all that some people are familiar with. For example, a phone can connect to one headset, or one music stream, or one of each, but not two headsets or two speakers. A PC can, however, connect to many phones at a time.
- You can hook up unlimited devices, no restrictions. (source - a Bluetooth Dongle tech-support)
False. You can usually pair unlimited devices on a host, but you cannot connect to them all simultaneously (again, think of the number of saved wireless networks, that aren't all connected at the same time)
- Only devices that support "multipoint functionality" can have multiple hooked up at once, and the choice of adapter doesn't make a difference.
Partly true. This only applies to client devices, such as headsets, controllers, keyboards, etc.. These limited devices can only connect to one host at a time if they do not have multipoint. A host can accept multiple clients even if those clients do not support multipoint.
- Only Bluetooth 4.1 adapters support multiple devices.
False. No idea where he got this from, it's plain rubbish.
- You can only use one device per Bluetooth adapter.
False. Pretty much everything in that entire statement is wrong.
So the final answer is yes, you can connect four controllers (clients) to one adapter (host) at a time. Even without the above information, it's fairly obvious as per @oldmud0's answer,
if [controller] uses Bluetooth, then how does the PlayStation establish a
connection to all 4 controllers with a single radio [if Bluetooth didn't support it]?