Presumably the neighbours you are referring to are houses next door to the flats, rather than other flats in the same block?
For FTTP to be installed in blocks of flats Openreach require permission from the owner of the building to install the fibres to each flat, if this permission has not been granted then it can't be installed - best you check with the property management.
I'm a little confused by the following, the two bits in bold seem to contradict each other.
....in fact anyone on the street on that checker show as ADSL only.
On BT's website my address shows as ASDL only. But next door can get fibre. I don't understand how.
I take it you are using the
BT Wholesale Checker, and then clicking address - do not use the postcode option. Then just enter a postcode and press submit and it will give you a list of addresses for that postcode to choose from.