They were developed and coded by someone so how can you be so sure that "someone" hasn't left any backdoors?

Open source code.
Don't be so naive. Who can compare the actual code running vs the published open source? There are people maintaining it, updating it, hosting it. It can be hacked too. The author or some malicious admin for example can edit or recompile the code adding backdoors and you will have no idea it's not the original one.
