I used a Little-Dot II+ as a preamp for a number of years with my Yamaha M-2, which is a Direct Coupled Amp. The Little-Dot II+ came with the same warning you described, yet it was never an issue in practice.
Most power amps have an in-line capacitor on the inputs that blocks ultra-low frequencies, below what the human ear can hear. A Direct Coupled amp is theoretically capable of passing any frequency from the preamp to the speakers, all the way down to 0Hz, which would be a DC (Direct Current) signal at that point. A normal audio signal is AC (Alternating Current). This is why the cone moves in and out. When a DC (Direct Current) signal is fed to a speaker, the cone will move in, or out, and stay there. This causes the voice coil to heat up despite the speaker not producing any sound. Speakers can be damaged easily if fed significant amounts of Direct Current.
I found that the only time any relevant amount of DC (direct current) was being passed from my Little-Dot into my power amp was right after the Little-Dot was powered on. I mitigated this by always making sure to turn the Little-Dot on first, and give it a short time to warm up before I powered on the power amplifier. Ultimately, no other precaution was necessary.