Please, define for us what is REAL TIME?
When the method was first developed in the late 1940s and for a few years afterward, the method did make the assumption that the ratio of C14 to C12 was constant. As a rough approximation, the assumption is valid. However, as an increasing number of carbon-14 dates were obtained, including many on objects of known age, it became clear that the assumption was not strictly true. This fact has been known to the scientific community for several decades and mathematical correction factors have been developed to adjust for the fact that the production rate of carbon-14 in the atmosphere has not been completely constant over the past few thousand years. In other words, modern radiocarbon dating uses a calibration method to correct for the problem that Major views as a critical weakness of the method. But curiously, even though these correction methods have been in use for several decades, critics often fail to discuss them. It seems clear that many do not study the method well enough to be aware of the use of these correction and calibration methods. The fact that the raw uncorrected dates must be corrected for the less than perfect equilibrium in no way invalidates the method. To use an analogy, if you had a yardstick that was only 34 inches long rather than 36, it would still be usable, provided that you knew the details of its imperfection.
Not to mention, C14 and other radiometric dating methods, even much more accurate are used in conjuction with other techniques to provide an overall landscape of support.
I have not read any details on this recent "discovery" in Israel, but if they have dated the remains to 400,000 plus years, my guess is that C14 was not the method used. Other, even more reliable radiometric decay models were most likely used.