come via BT at some point - BT wholesale sells the service to ISPs like Tiscali, who then sell it on to you.
The £15.99 service is a 150kbps connection, and some people are concerned that this is called 'broadband' at all - the common conception of a broadband service seems to be that it is at least a 512kbps connection. Leaving that debate aside, the £24.99 service is a 512kbps connection, and like all ADSL services it needs a BT copper telephone line.
I have no way of knowing why you can't have the service if you live within range of an ADSL enabled telephone exchange - presumably you live within the 3.5 kilometre range? That figure is for line length, not 'as the crow flies' by the way, so every twist and turn of the cable as it makes its way to your house is included in the calculation.
Incidentally, on the subject of that 60% service claim, what the company actually says is this:
"Approximately 70% of UK homes are currently on Tiscali Broadband enabled telephone exchanges"
Note that they say this percentage is on 'broadband enabled exchanges' - that doesn't mean that they can all get the service, many of these people will be out of range.