You are 100% right mate, as these were rated at a lowly 2200mAh 35C 4S, which is why I chose them… for less output and shorter runtime than the stock OOTB supplied 2500mAh 30C 3S battery that barely even raises a sweat, along with ALL the other batteries that I run through it at the same pace!
The two 2S OVONIC’S that I “Doctored” into a single 4S, each with much larger 5500mAh 100C outputs don’t have any issues whatsoever, and either do the smaller old TURNING 2200-3000mAh 3S 30-40C batteries.
You are correct in saying that the electrical system (motor/ESC) cannot “pull” more than the batteries can provide, they are just a “tap” that opens up, and the batteries are just like a bucket of water and the power leads are drain hoses that allows as much water to flow out of the bucket as much as it can “flow” out of that “tap” once it is cranked open.
This is were the “C” ratings are meant to determine the size of the drain “hoses” that come out of the bucket (battery)…the larger the “C” rating, the larger the “hose” and the more water available to flow through the “tap”.
But from day one, there was absolutely ZERO difference in speed/performance between the 30-40C rated stock or TURNING batteries, which is an immediate telltale sign that the “C” ratings are bullshit on those apparently 100C batteries that should have “flowed” twice the amount of power to the electrical systems!
But that’s what that RC Battery Expert has proven time and time again throughout his testing of all the batteries on the market… there’s NO laws regarding whatever claims cheap Chinese battery makers put on their packaging and are all trying to outdo each other with rediculous mAh and C ratings to try and get an edge in the cutthroat LiPo battery market with their claims. 
Unfortunately even the most trusted battery manufacturers such as Turnigy and others have also reduced the quality of their products just to try and stay competitive in the same market now flooded with much cheaper and higher claimed output batteries taking the market share. 
Hence why I don’t believe shite and rely purely on research from actual electronics experts testing such products, and obviously shouldn’t have believed all of those reviews from online channels who received OVONIC batteries for free to review. 
If you have old TURNIGY batteries, look after them, as they are much higher quality than ANYTHING being produced these days. 