That is a good summary. Some radars use phase shifters, and some true time delay elements. They are equivalent for narrow bandwidths, but the true time delay is needed for wide bandwidths.
In case anyone else is interested: the distinction between phase delay and time delay comes into play if bandwidth is large as you say, but in one more case as well. If the array is large enough that the time delay across the array is on the order of a symbol period you must use a true time delay. If you use a phase delay instead of a true time delay, energy from separate symbols will be added together to make the final bit decision and the resulting ISI will increase BER.