Could someone who understands the radio technology please explain why using time-of-arrival and phase tricks with existing WiFi and Bluetooth signals is "wide-banded" in any way?
The wider the bandwidth the faster the rise time of each 'pulse'. The UWB standard allows for a known preamble sequence upon which a particular symbol is designated the ranging pulse. By each pulse having a rise time in the picoseconds it allows for an exact time of arrival to be measured. Exact timestamps can be recorded on each side of the transmission giving the final bit of information needed to calculate tof.
edit: clarity of last sentence
WiFi channels can also be 80MHz (which my laptop is currently connected at) and 160MHz (which is still a bit rarely supported), but your point still stands.