That is only possible if you don't use any FI accounts and don't have any taxable income.
I don't deny that there could be some country that defines you as tax resident if you use FI accounts or have taxable income. I don't know what these countries are, but I'd quite like to know so that I can avoid them!
Of course departing citizens of some countries absolutely do have this risk, but again we're looking at a case where they are still tax resident somewhere, so they're not PT as I understand the term.
So to make things easier, I'll just pick two jurisdictions that I have some understanding of: Georgia and the UK. I can have bank accounts in UK, I could have family, work, property, income in UK and still not be tax resident, depending on the number of days and how many of ties I have. I can have bank accounts, family, work, property, income, etc and still not be tax resident if at no point in the current tax year, I'd spent 180 of the last 365 days on Georgian soil. I could easily be tax resident in one, both or neither of those countries.
The parts a, b and c you refer to live inside paragraph 2 that applies if I am tax resident in both countries. A PT is tax resident in neither, so paragraph 2 does not apply and neither do its sub parts. Someone should make a flowchart to help understanding of this.
I'm not sure if we're still on topic for "UAE unveils tax residency criteria", but this issue crops up quite often and I do believe that it ought to be addressed. People worry about "getting tax residency" and often fail to understand that this doesn't mean they lose their original tax residency.