I think it's to try and mitigate fraudulent documents being provided. The reason behind this is it is a lot easier to edit and forge online documents than physical ones. Of course, I am not saying it's impossible, but it's just another step to try and mitigate these risks. That's why they require online bank statements to be stamped by the bank.
Yes, that's exactly it. They need to be sure that you haven't tampered with the statements and changed the figures on them, which is much easier to do with online statements than with ones posted to you.
(bb) Payslips must be:
(i) formal payslips issued by the employer and showing the employer’s name; or
(ii) accompanied by a letter from the employer, on the employer’s headed paper and signed by a senior official, confirming the payslips are authentic;
So if the payslip is online and it contains the employer's name then I am given to understand this should be fine without the letter of authenticity.
I have also provided my six online payslips but they have the company logo on the payslip and shows my employer's name.
No, that's not true.
As it says above, the only payslips that are acceptable without a letter are ones that are formal... i.e. payslips that your company has printed on official company paper and either handed to you in person, or mailed to your house.
If the payslips are online, they are not considered official/formal and therefore, they MUST be accompanied by a letter from the employer, printed on company letterhead and signed by a senior official, confirming their authenticity.
This is for the same reason as you need the bank statements to be verified, because online payslips could easily have been tampered with, so each one must be authenticated by the employer in a letter.