Hi,
I just finished a partially self-funded PhD in the UK (partially because my tuition fees were covered under my research grant) and I haven't met any other self-funded students in my time, so I'd say that percentage is rather low. Though there might have been some as others never really noticed me as being self-funded. If it ever came up then the answer to it was a unanimous 'wow'.
I agree with you in seeing it as a good investment. Before agreeing to it, I made an extensive finacial plan of how much money I had, how much money I was getting on a regular basis etc. and gave myself a generous monthly budget (£800pm, generous as in the end I averaged on £730pm) making sure that at least 10k would be left over in the end as an emergency fund. I do not know about you, but I had all the required funds from the start. I would not have started the PhD if I would have had to rely on part-time income or taking on a loan or if the fees hadn't been covered as I would not have been able to do so without breaking the first two reasons. The part-time demonstrating I did at the university were nice little extras.
I would not think of myself or you as being abnormal! If at all it shows that you are or will make you more determined. When it got rough (it will) and I doubt myself it was the thought of having wasted £40k+ that helped.
The basic question that helped in the decision making after considering the financial situation was whether I would regret not taking the opportunity and the answer was yes. The funding situation of others should not matter. As long as you are determined to work hard and live a very frugal life (in my case living below the minimum living cost in the UK of £1120pm), go for it.