How Would you Define a 'SOLO' Climb

Kili is not a climb. It's a trekking peak.

A solo climb is first of all a climb(as opposed to a stroll up an easy peak summited by 70 year old German pensioners on holiday), and second it's solo. Where else are you required to have a compulsory guide?

To get a permit for Nepal's trekking peaks (some of which are extremely difficult climbs) and also mountaineering peaks, a guide is compulsory. In reality he is actually "guiding" just the approach trek and also has the job of being the whistle blower to the government if trekkers do not behave as per climbing rules. They are not prepared to climb anything technical and can and will stay at the base camp if the client so wishes. So at least in Nepal it is perfectly possible to attempt any mountain "solo" if the climber so wishes.

I would define a solo climb one where the climbing from BC to the summit was done without any help from others. On some routes like the Everest standard routes both from the south and the north this is practically impossible, as there are trails, routes and fixed ropes everybody is using anyway.

There are many countries where you cannot climb peaks, or only some peaks (for instance not above 6000 meter) on your own. It's actually the case for ALL the countries in the Himalayas.
In some cases, it is possible to climb them in a clandestine way (some climbers do it, including in Nepal).

What does climbing on your own mean? About one third of the trekking peaks of Nepal are so difficult that there are no Nepalese guides who can climb them. Recent climb on Kusum Kanguru, a trekking peak, took 9 days of alpine style climbing to reach the summit, and 4 days of down climbing. Only a handful of people in the world can accomplish that. None of them are Nepalese.

Like I said, going to the base camp with help, porters and guide, does not mean that the climb itself (which is considered to happen from BC to summit, approach does not have to be "solo") can not happen solo, and there is no requirement in the rules that the guide must accompany the climber all the way, and on most mountains they would be unable to do that anyway.