"Total pedestrian fatalities dropped from 49 in 2011 to 44 in 2012" [1] Singapores' population is ~5 million[wikipedia], so the odds of being killed by a car for the total population is ~0.00088%
For a comparison let's look at NYC, which has roughly double the population within City Limits (~8 million for NYC):
"From 2002 to 2006, 843 pedestrians were killed"[2] That's ~211 deaths per year. Making the percentage odds ~0.0026375%
So you're about 1/3 as likely to be hit and killed by a car in Singapore than NYC. That's fairly significant, but there are a couple things to point out. NYC does have a significantly higher population density and I would assume it has a higher amount of vehicle traffic.
I think overall while it's clearly less likely to be killed as a pedestrian in Singapore, I wouldn't exactly call it "rare". And while I'm no professional on Singapore, I don't know why you characterize Singapore as somewhere that doesn't have large roads or many vehicles (There are 965,192 vehicles in Singapore[1]). Also I don't think CCTV is nearly as ubiquitous as you think, from the few news articles I've read they probably only have a few thousand with more only starting to roll-out recently[3][4]. It's certainly not up to London standards, and I doubt even there ever single pedestrian death is caught by CCTV.
[1]http://driving-in-singapore.spf.gov.sg/services/driving_in_s...
[2]http://www.nyc.gov/html/dot/downloads/pdf/nyc_ped_safety_stu...
[3]http://www.safetrolley.com/latest-news/singapore-police-inst...
[4]http://www.asiaone.com/News/AsiaOne+News/Singapore/Story/A1S...
"With a population of 5 million, Singapore has one of the world's highest per capita execution rates. While official figures are not produced, according to Amnesty International there have been at least 400 executions over the past two decades." - The Guardian, 2010-11-16, http://www.guardian.co.uk/commentisfree/libertycentral/2010/...
In the short time I have lived in Singapore, there were two kids killed by a truck, and I've seen two or three roadside signs appealing for witnesses to accidents with serious or fatal injuries.
So it's pretty much like other places. People can get hurt, and big brother is not all-seeing just yet.
And when were they documented the first time? It's much more plausible to believe that you are paid by the Chinese government to spread that rumor than to believe what you've written.