VERY definite input sensitivity matching

Is it in fact of utmost importance to match a source’s output voltage to be less than or precisely equal to the exact input sensitivity of an amplifier?
My amp’s input sensitivity is 0.4V so I run my DAC to it attenuated to a (measured) bit over 3V, with the amp’s potentiometer at max so as to minimize its influence in the circuit. It sounds very good this way - however, what if the DAC had a (nearly) exact 0.4V output? Would it be better or worse, worse such that at the very threshold, a slightest deviation over 0.4V could make the amplifier clip when fed with full level signal at that instant? I don’t know how much a modest quality modern DAC can have such unwanted deviation in voltage. Negligible?
Could the amp clip when fed 0.4V for other reasons with the pot maxed? I understand that there is always a reactive, uncertain jungle involved with any system that isn’t lab-grade from the AC up. So just to be safe, should I keep the voltage a bit below the input sensitivity?

By the way, is there any mechanism in an amplifier’s workings that could potentially make its input sensitivity vary, or are its determining circuit properties “hermetically” separated (so to say) from the workings of the amp’s workhorse circuitry? I’m asking if I can trust, absolutely, that it’s a constant…

Then again is anything a constant in our systems that are made at minimum from “quite a number” of components whose reactivities can’t ever fully be tamed to absolutes? Oh and that we can’t (yet) quite live and prosper without the necessary evils of cables? I guess monoblocks with mono DACs inside (and yes, sources included within each…), connected by straight cold weld to the speaker terminals (assuming they are interspaced to match) could get us quite close to no cables?
Oh, is this philosophy now… why not.