I have never bought or even used a WiFi-based printer, but wanted to add the ability to print directly from a number of laptop/portable computers that were in WiFi range, on an ad-hoc basis.
The optimal situation would be to power-on the printer in different places (places that don't have WiFi), and people that have the a laptop and were within the printer's WiFi range could use the printer. Although this question is NOT about the program the people will be running on their computer, explaining the software scenario might help visualize the intent. The idea was that the user would start a custom application which would silently scan active Wifi connections, recognize the printer by name, and connect to it if printing was needed.
To cover the above scenario, the WiFi device (computer) would have to connect directly to the WiFi supplied by the printer. The printer would need to be password protected so the device, which has been supplied with the password, could connect, but direct access would be prevented. Note that this is different than getting connected to a WiFi network that has a printer that is part of that WiFi network. The question is about if there are WiFi printers that do not require an underlying WiFi network.