Nope, quite the opposite (to both statements).

I'm sure you know what Damping Factor (DF) stands for. But if not / for other readers: DF = ratio of the load (speaker/headphone driver) impedance divided by that of the amplifier's.
Why DF matters?
A speaker drivers is an electro-mechanical system. Ever tapped on different speaker drivers before and noticed how each produces a different "thud" sound? Well, that's due all the various characteristics of the driver - i.e. cone material, cone weight, spider and surround tension / returning strength, and etc. The speaker cabinet will also affect this quite a bit (though with headphones, this is probably not that important.) The point is, when you tap on a driver, you displace it from its idle/resting position. The spider and surround tension return the driver back to its idle/resting position, but not instantaneously - that's physically impossible due to the weight of the driver. So the driver will "wobble" back and forth "a little" before returning to its idle/resting position. Essentially, it's analogous to resonance ("ringing") in R-L-C electrical circuits, and every speaker has its own distinct characteristics. Now, when this "wobble" back and forth happens, don't forget the voice coil is moving through the magnetic field in the speaker's pole piece, thus generating back-EMF. If you provide a low-resistance path for this back-EMF, you can greatly reduce the "wobble" self-resonance of the speaker driver / voice coil... and that's the key here! - you want an amplifier that has as low of an output impedance as possible, so that any self-resonance "characteristics" of the speaker driver (and its cabinet) are reduced to a minimum. The idea is not for the speaker driver and its cabinet to add too much of their own self-resonant characteristics... through it's impossible to reduce them down to nothing. And this is why no two speaker drivers or cabinets ever sound the same.
Now if you wonder what the above has to do with headphones... well headphones are pretty much the same thing as regular speakers, but just a smaller version. You might think the small mass of a headphone driver is insignificant, but it's not! Same physical principles apply as to regular speaker drivers, and the results are measurable.
With that said, here is one of the studies that I found a while back on this matter (I built a headphone amplifier for my senior project in uni, so this was part of the research that went behind it.)
https://www.badcaps.net/download/?id=9c3883f3
If you've read through the above study, you can now see how a series resistor with the speaker/headphone driver can actually impact its sound characteristic. Note that more output "distortion" doesn't necessarily mean you get less bass output. If you look at Figure 5 of that study, you can see that the bass output from 40 Hz to 160 Hz increased by more than 0.3 dB with the series resistance driver than without it. Sounds like a good thing, but it's not - it's the headphone's own driver that's adding its own self-resonance to the output sound. If you like more bass, then that's a good thing. But what if you use a different pair of headphones that has the opposite effect? Then you could loose bass output. So the series resistor could work in your favor or completely against it, depending on the headphones used... which is not a good thing. If you want "repeatable" results and less deviation between different headphones, then getting rid of the series resistance is the key.
So going back full circle...
You are 100% right in wanting the lowest possible ESR when it comes to output coupling caps, because that will work to reduce the series resistance on the output. But again, with virtually all motherboards using series 10-100 Ohm resistors, your drop of a few milliOhms using low ESR caps cannot produce measurable difference. If it did, then the old output coupling caps really must have gone very high ESR (more than 5 Ohms.) And even then, you'd only get a measurable difference if you drive a low impedance load directly (i.e. headphones.) An amplifier with an input impedance in the KOhms range will simply not care the slightest bit how bad / high of an ESR those output coupling caps have. However, leakage current becomes an even bigger factor here... and that's why it's important to use caps with low-leakage current in audio. So "audio grade" caps are not complete "audiophool-ery"... but they are quite over-priced for what they are and won't make a difference in every instance - that will depends on the circuit design too.
And yes, I'm speaking from experience here, too. I've upgraded the caps on a few motherboards from the original 100 uF GP series to 220 uF low-ESR (Nichicon HE / Chemicon KY.) When driving headphones directly - yes, it mattered, because the higher capacitance of the output coupling caps reduced the low cut-off frequency approximately in half. But when driving my headphone amplifier, it didn't make squat of a difference.
, there goes the audio chip output when the caps go short-circuit.
because the computer was under the table, i had to shine a usb torchlight to make sure the connector was lined up in the header properly and gigabyte decided to put the header right up against the rear panel audio jacks grrr! so i fired up the system, made sure the right inputs and outputs were unmuted, made sure front panel jack detection was already disabled then retasked the green front panel jack to line out and the pink front panel jack to line in. then i put on some skyrim music and the dtv set top box audio output into the mic input front panel pink jack and then the moment of truth! i plugged the speaker audio jack into the front panel green jack and i had my ears blasted with some good skyrim music. hooray it works!
getting my ears blasted with some skyrim hd audio was a good thing also to boot, so no worries about my hearing. hahaha!
oh and the mic jack also works in receiving the dtv set top box audio. 

what did we say about hoarding too much stuff and depriving others of them?! *cough* socialism *cough* lol! 
and i've read online reviews of some people saying their creative card died due to bad caps. considering that the creative cards have at least 20 caps on them, a full recap is much too tiring work esp. since the 5-6mm audio caps are soo much smaller that the 8-10mm caps on mobos, i decided i just dont have the dexterity to do a full recap of a creative sound card.
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