As much as I want to think that's true, that's not at all how I read it, and apparently a lot of EU politicians are reading it. It's more that the grace period starts soon , and it will end soon after UK leaves, effectively this not being any offer at all.
Regarding the status of EU citizens there are also a couple of other things to keep in mind.
The CSI (Comprehensive Sickness Insurance) Trap:
If you're an EU citizen in the UK, who is self sufficient (e.g. a partner of a UK citizen, who does not work) and you do not have CSI, then your time in the UK does not count towards the 5 years.
This is also true for students. In addition to that, Universities have had no policy informing students about the need for CSI.
A question here would be, do the years in employment count towards 5 years of residence, if at any time you have been the victim of the CSI trap?
EU courts don't cover you:
Even if you get "settled" status in a post-Brexit UK, your rights will not be backed by EU courts, but by whatever Theresa May's government decides to take over from EU legislation through the "Repeal Bill".
This means that there's no clarity at all how your continued stay is governed after Brexit.
Can you leave the UK for a certain amount of time before they make you illegal?
How much do you have to earn in order to stay legal?
How will new immigration bills effect your status?
So yeah, EU citizens in the UK should be aware that the "offer" by Theresa May has not given them any kind of assurance about their status in the UK, especially not in a post-Brexit reality.
If they want to make you illegal, they can.