Probably they are referring about the 6K usd market price stabilization though generally bitcoin will not become stabilized due to its current system that is decentralized. It may be better if we will not consider bitcoin market price stabilization. I agree with you OP. We should stop calling bitcoin stable in its market price.
This is it. It will take years before bitcoin becomes even remotely stable but because the market price has been sitting around the same price these days, people say it is stable. Besides, if it's already stable, then how come nothing changes in the market? People say stability will make companies want to adopt bitcoin but has it happened? No. Absolutely not yet.