OP you are quite right, and it is not fair or reasonable for them to expect a legitimate space that is supposed to be for anyone who needs it to be left free in case they want to come back. It is not their bit of road. You were reasonable, they were not.
LaurieFairyCake it doesn't get more cars off the road, if a space on their front garden means the loss of a space in front of their house. If they were allowed to get away with this it effectively just means they are being allowed to monopolise a space which they have no more right to than anyone else.
In a previous house I lived in, there was a row of three terraced houses (we were in the middle one) and enough space for three cars to park on the road. However, there was a double yellow line on the road in front of the left hand neighbour's house and a little way across some of the front of ours, and the three cars therefore went in front of the right hand side of our house, in front of the right hand neighbour and the gap between the end of the terrace and the beginning of the next row-of-three, where the free-for-all parking stopped as there were a couple of disabled-only spaces belonging to the occupants of those houses.
It was all fine for years and we easily shared the three available spaces until the right hand neighbour suddenly decided to remove the front fence and park their car on their lawn - with the gap in such a way as to remove two of the three parking spaces because it was at the half-way point between space number two and space number three.
They didn't respond well to our suggestion that this wasn't fair and we ended up having to lodge an official complaint to the council, who completely agreed with us that this behaviour wasn't on. They said that a dropped curb would be subject to planning regulations and if they applied it would probably be refused as we their neighbours would legitimately object on the grounds that it would constitute an unfair restriction on the already limited available parking.
(they ended up leaving the area not long after and were replaced by lovely people, so it was all alright in the end)