First, even if the radio won't be damaged by 3:1 SWR, it will certainly have to cut back the output power, perhaps to 1/10 of full power. So the tuner will be what allows it to function correctly even with a modest SWR antenna.
The problem with operating a tuner with high SWR is that for some antenna impedances, typically the Low R High C of a short whip, it will generate very high Q solutions that result in very high circulating currents. These can overheat the inductors. Even if the tuner is not intended to tune a short whip, and won't have enough series inductance to do it at low frequencies like 3.5 MHz, at a higher frequency like 14 MHz there might be accidental tuning solutions that do seem to work and provide a good match.
For example (without pulling out my calculator) - if the antenna is 3:1, being about 20-j100 Ohms, this can be tuned to resonance by an inductor of about 1+j100 Ohms, and the inductor loss will be a small fraction of the total power.
But if the antenna is 1-j200 Ohms, the tuner might manage to match this using all its inductors, say 3+j300 Ohms, and then some parallel capacitance to bring it back near to 50 Ohms. In this case you can see the tuner will absorb 75% of the transmitter power, which is not ok.
And the examples above could happen to the same tuner, at different frequencies, depending on the antenna. The tuner doesn't measure the antenna impedance, it just searches for low SWR.
A clue that the tuner is overloaded is that the SWR will climb up while you are transmitting, as the inductor heats up and changes shape.
Finally - the antenna you link to (seems too good to be true, for a simple wire antenna) says it shouldn't require a tuner, but the SWR might go up to 2:1 in places. This are exactly what the rig's built-in tuner is designed for.