Um - no. Check the specs and then you can know for sure. FiiO very kindly publishes theirs. The X5iii outputs (via lineout) 1.8 Vrms (or about 5.1 Vp-p). They don't quote current, but as Relic points out - it'll usually be low fixed current. The line-out voltage is just over half of the voltage the X5iii will output at full volume via the SE headphone out. Its not going to melt any drivers.
The quote has nothing to do with headphones. They're talking about speakers. And putting that sort of low impedance load across a kilo-ohm line-out won't generally damage the speakers, but it could short the amp.
You should be able to do it - but I wouldn't. The issue is that the line-out wasn't designed to output to headphones. It has a 10 Kohm output impedance, and will be current limited. Despite the loudness (because of the high voltage), its unlikely to power any load properly because its not designed to. A line-out is a low noise output designed for use with another amp. You might call the result a different sound - but why would you intentionally under power a pair of headphones. And if they are low enough impedance (unlikely), you could damage the amp on the X5iii.
Just use the headphone out, and engage EQ or Viper if you want a different sound