TLS is correct. The power supply has very much to do with an amplifier's ability to deliver current. Better amplifier designs do a better job of dealing with low impedances. No doubt about any of that.
I'm going to tell you, however, that most amplifiers are conservatively rated in terms of their ability to drive low impedance load. They are so rated primarily for legal reasons because we all know that audio component manufacturers love to stretch their specs. This is one spec they don't stretch because, at the extreme, it can result in equipment damage, not just a failure to meet a spec. Personally, I have not encountered an amplifier that won't drive a 4 ohm nominal load to normal listening levels without overheating or distortion. I'm sure there are some, but I haven't encountered one. I've tested scores of them over the years. Yes, it is always possible to abuse the equipment-exactly what the lawyers are concerned about. I'm talking about normal use. Except in extreme situations, I wouldn't spend much time worrying about it. I've heard my own 6-ohm-minimum-rated receiver drive electrostatic speakers to very loud levels without clipping (o-scope measured.) Those speakers dip below 2 ohms at some frequencies.