It doesn't need to be connected to a server if the meter is periodically attached to a computer that downloads the data.
That said I have no idea if that's something they do. I am now going to try to find out.
--edit-- it's not easy to find data on this. So far I have found out that most taxi meters have to be taken in to an office or depot to get the fare-structures updated...
There's no requirement to log information (let alone store it for future upload), only that the taximeter is audited (for distance accuracy) every 12 months or so, and that it has updated fare structures (which modern ones do over GSM/GPRS).
"Every driver must accept card and contactless payments and provide receipts for those payments upon request.
All taxis must have a fully working TfL-approved fixed card payment device fitted within the passenger compartment - a handheld-only device will not be sufficient to meet the licensing requirements. Any taxi found not to meet the requirement will be issued with an unfit notice, which will remain in place until the requirement is fulfilled and the vehicle is presented for inspection."
So it looks like either the story was a little old, or the cab was in violation of the rules.