I have a big problem with this too but its actually even more complicated- it turns out PAF is not actually a full set of addresses - its a set of delivery addresses. There are actually properties (such as the one I live in) where there is only 1 delivery point for multiple ‘real’ addresses. PAF lists these as multi occupancies but you have to pull a second data set to get them.
A real example:
I live in flat b in my converted house. Our PAF delivery address is 27 b-d (which is actually 3 flats)
There are so many providers out there who have integrated PAF and believe its the real legal definition of where I live - makes it very difficult with banking, telephone lines, internet etc. Santander originally would only let me pick my address from the PAF list (e.g. forced me to choose 27 b-d) - then they made me send a ‘change of address form’ when I told them I actually live in flat b so it could be manually processed!
Interestingly given how many different address formats there could be for the same address this is why when banks do address verification as part of a transaction (on the billing address) - they just match the numbers in the address plus numbers in the postcode - a good approximation and handles different ways of writing address