So is it just a suborbital plane that can launch something high enough where an additional small booster can put the payload in orbit?
It's the BBC, so I'd say it's an averagely written article in their context.
Noticeably, the point of the Skylon and SABRE is that it's possible to use a common engine core in airbreathing and pure rocket mode, thus potentially generating weight savings.
I'm sure someone sat down and did the calculations. I have this feeling that a lot of the times when you actually sit down and work out the math for a range of assumptions, you generally come down to 'eh, maybe A, maybe B, so may as well try A'.
"power units that work like jet engines at low altitudes and slow speeds, but then transition to full rocket mode at high altitudes"
and
"Skylon itself is designed only to go a few hundred km above the Earth, so it would need an additional "upper-stage" module to push the satellite into its final, 36,000km-high orbit."