Some if these could use a bit more detail.
"All DDR3 is the same" ... Just wanted to mention that in close on 25 years managing and participating in web forums, can't say I have ever seen this one put forth for either DDR3 or anything else. There are numerous differences, some matter not at all, some matter a little, some can matter a lot. It's crapshoot, but the odds are pretty good if you don't have a lot or large differences.
"Mixed DRAM Runs At The Speed (Or Timings) Of The Slowest DIMM" - I think this is just poor wording of the intent when this one is used. More correctly, it's much like video cards .... one card is advertised and guaranteed to run at one speed, the other a little bit faster. Like RAM, in SLI / CF you have a pretty good likelihood of setting them up to run at the lower of the two speeds. You have a lesser change of getting them both to run at the higher speed, tjo it's worth trying; that slower advertised card may have some headroom that was previously untapped
You also have the issue that 2 cards put more of a strain on the PSU and when that extra load is present, voltage stability suffers. Your faster card, with more voltage variation may not be able to handle the same OC that you had before the 2nd card's load was added.
Same w/ RAM ... one would presume that if a set of RAM was capable of a higher speed, it would have been binned and sold at the higher speed. As vendors respond to the variability of supply and demand, we may see better quality sets sold at lower rated speeds, which we can attest to by reading how many reviews in which the tester was able to get significantly higher speeds. So when someone says "will run", I have always taken it to mean "the likelihood is that it will be able to run at the less demanding of the two speeds / timings. As always, no guarantee. As it is, your likelihood of getting 2 1600 sets to work together is much higher than getting two 2400 sets to do the same. Success will be better at 1600 / 1600 and 1333 / 1600 than it will be at 2400 / 24500 or 2400 / 2666
I haven't been asked to do many upgrades since Sandy Bridge days (when some folks were still buying 2 x 4GB) but back then at 1333 / 1600 and 1600 / 1600 matchups, our success rate was well over 90%. And those difficulties came usually resulted from having different module OEMs. In the last 3 years, I'd say 9/10 builds started with 16GB and those who chose 8GB are still content, so don't get the opportunity any more.
"Just add more DRAM" .... I'd add that the most common cause if mismatch results from the maturation process of the production lines.... When DDR3 first broke 1333 was the most commonly purchased speed, as productions lines matured and yields improved this grew to 1600 and of late we have seen great yields on 1866, 2133 and now even 2400. As lines mature and yields improve, required voltage also comes down.
Initially, a vendor will usually buy their lower speed modules from one vendor and then sign on with a higher quality vendor to fill their needs for higher speed RAM. Over time, the lower price vendor's yields may be sufficient to supply their demand for the higher speeds. So we wind up with a situation where a vendor's product from 2012 will use one brand of module and one from 2015 will be from another. That presents quite a challenge for compatibility.
This can be particularly frustrating as one version from January 2012 and one from November 2014 might work fine and then one from November 2014 and January 2015 might have no chance in "H E double sticks" even tho every one of them has the exact same model number. Sometimes you can notice this by a slight change in timings. Several vendors offered 2400 at one time at 10-12-12-28, nor those same models are 10-12-12-30 or 10-12-12-31.
"It’s Cheaper To Buy Two Sets Of DIMMs Than Larger, More Expensive Sets" That's not a myth, at least not as stated.... they are cheaper. The "myth" as stated doesn't say anything about working
. They may not run together at advertised speed but they are still cheaper.
"There Are Only A Few DIMM Manufacturers" .... given the limited 2 sentence attention this subject got, the topic should have been eliminated.