It does not have so be 8 ohms or above. My speakers are 4 ohm, but they are very, very flat and very well designed. I bought them to use with an ss amp. The first time I heard them with a tube amp, I promptly sold the ss amp.
The statement with emphasis added is false. If you want the most out of your tube investment dollar, stay well away from speakers that are 4 Ohms or less, even if they have a flat impedance curve.
To drive a 4 Ohm speaker you need a 4-Ohm tap on the output transformer. When you use that tap, the amp will make slightly less power and may well lose an octave of bass. Distortion will be higher too.
Even if you have solid state amps, if high fidelity is your goal, 4 Ohm speakers are a bad idea, simply because all amplifiers, tube or solid state, make more distortion into lower impedances.
As a special rule of thumb, if you are looking at an '8 Ohm' speaker that employs dual woofers, ask the manufacturer if the woofer array is also 8 Ohms. Its quite common for speaker designers to put two 8 Ohm woofers in parallel, producing a 4 Ohm load in the bass, while the rest of the speaker is 8 Ohms, and then say the speaker is '8 Ohm compatible' or some such nonsense.
If in doubt, avoid speakers with dual woofers unless you get a very good audition in your home.