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You guys read the Web which is good, but fail in engineering interpretation, so you are wrong and others repeat this rubbish.
The figure you are quoting it is a relationship between state of discharge vs battery voltage on the open circuit. It is meassured after disconnecting load and let the battery rest for half an hour or more (I don't remember exact figure), as depends on the load the battery can get hot. This is very accurate if temperature of the battery taken into account as well.
On the other side there is no way to determine state of discharge during discharging, unless the battery current and other parameters are constantly meassured and evaluated. It is not happening in any UPS you can buy.
You can also see occassionaly a figure SoC vs. voltage during discharging, but it only applies to a brand new battery of a given make and capacity. This figure is given as an example for developers, but not for referals. It is critically dependent on internal resistance of the battery and this parameter very depends on the age of the battery, it is also very unstable during breaking sulfation.
In summary, developers set cut-out voltage based on the battery capacity, chemistry and make. It is made experimentally between 10V and 10.7V for the battery they sell with UPS, so it is safe. When you replace internal battery with a much larger one, it is obvious that this assumption breaks and a cut-off is delayed during large loads due to the smaller internal resistance of the large battery. The small UPS will likely trigger cut-off first due to the other condtion, like a heat generated inside the transformer.