Speaking from an analytical point of view -as I am not one who has tested these wheels nor do I have substantial knowledge in regards to material engineering, but rather from a point of view of somebody who has done their homework on this subject before.
I think I can say from what I have discovered, ROTA has been given a bad rep for a few reasons.
As soon as some tragic event that questions the validity of the company occurs and then is posted on the internet, the logistics no longer matter. There are too many haters, trolls and elitists out there who don't give a crap and consume every bit of evidence to support their cause.
Rota's are not the top of the line wheel manufacturer, so when viewed in comparison to manufactures such as BBS there really is no comparison, henceforth more internet friendly chatter.
I have a friend who was once endorsed by Rota.
He has actually encountered problems like the ones you have seen in the pictures. Does he continue to support them? Yes.
Why?
Well, he happened to be very involved in the street racing scene over in holland back in the early days when it was just catching on. He happened to be sponsored by a local garage who had been given some gram light rota prototypes, who then gave to him to test. They were not designed for his car or the conditions that he was driving in (-20 deg C) and unfortunately the spokes snapped, on more then one occasion.
Now, the logistics here are that he was given a "prototype wheel" to test out and he did that to the best of his ability but unfortunately we all have daily commutes too. Needless to say, that SHOULD not have happened but there is too many uncertainties to blame it on the company itself, even though that is the case.
If he had been like most MR members, he would have posted that up on the net back on 03/04 or whenever and by the time we see that picture today, it is merely referenced for proof that rota is shit.
The reason he stuck with them was for a few reasons: he was compensated at the time for that mishap, which included more free wheels and also because he was tight for cash. In theory to him, rotas displayed a perfect balance between price, style and weight (since they are alloy) which is honestly what they are intended for in the first place.
On another note, you mention that they are used for Toyota's as the OEM wheel manufacturer. While I cannot find any conclusive evidence that Toyota as a whole chose to get their oem wheels made there, I have found that Toyota AND Daihatsu's philippine division did in fact do this.
If you take a look at Toyota's current lineup: the yaris, the corolla, the camry...etc it's easy to see that none of them are high powered vehicles, therefore not as much stress and torque would have been exerted on the wheels compared to a high performance car that chose rotas as an aftermarket solution.
At the same time, it is important to note that large manufactures choose to cut costs everywhere they can, including wheels. Most oem wheels are gravity cast, low pressure if you will. So when toyota went to Rota and said "build us wheels" Rota did not have to go out of their way to infact purchase a new division of machinery or purchase lower quality steel, which would obviously elevate costs in the contract. They asked them because already created their allow wheels in that same manner, again cutting costs.
To add, since they are of alloy construction, this reduced their weight, while maintaining the same structural design as those of the other oem wheel manufacturers. With reduced weight, slight added benefits are added to the cars specs sheet, like increases fuel economy(something toyota strives for) which also means less emissions (long term) On an idividual car basis, its not measurable, its small but as a company as a whole, they are saving money and reducing their CO2 blueprint.
So when somebody tells me ROTA IS SHIT BRO, I tell them: well thats relative to the type of driving I do. If I do daily and moderate/spirited driving on the roads then they look alright, weigh less, which make the car that much more fun to drive as its a bit faster and fuel economy augments too, due to the overall lower center of mass (very minor though)
If I wanted to go out and thrash the crap out of my car at a skidpan or at auto-x then I would agree they are a must avoid, due to the grade of their build.
Also by looking at their companies origin from the Philippines, quality hasn't been that area's number one goal.
All of this is needless to say, would I recommend ROTA? I'm not sure, all the facts I have come across present valid arguments and if the person I'd recommend them to was doing normal driving then I don't see why not...BUT at the same time, all the pictures on the internet and all the hate going around places an aspect of fear in my mind and I wouldn't want to be held accountable JUST incase. But since I am confident in my research I would recommend them for guys who want a bit of flash and functionality without a huge price on their DAILY rides only.
I would NEVER place them on a high powered car for obvious reason: they are too light and cannot take the pressure exerted from certain cars which is due to their design and casting of build materials and at least they are honest about that. So when people do this and complain, well buddy, you shot yourself in the foot. You were too lazy to do a little research.
At the end of the day I would prefer not to cheap out on wheels, even if they are ok but not everybody is in that situation to do so, money is tight nowadays.
my 2c