I've often come across websites that have hard coded their logo into the banners some how, I don't know the technical lingo for it.
But I've always managed to dig into their code and retrieve the link to the logo - I may have needed this for an approved piece and waiting on their logo etc or they couldn't provide it.
There's no way to stop anyone stealing your work when it's online, musicians face this concern on a daily basis, as do movie producers etc. Or anyone that puts any form of art on the internet it's likely to be copied and distributed for free by the non-conformists to society etc. etc. etc.
Basically, if you use an image for a design and then it's found out you didn't have the copyright to it then you're open for a fair law suit.
If you create something, right from the beginning you own the copyright.
You cannot change a design by .00001% or even 99.99999% and claim it as your own - that simply is not accepted by law, there was a thing a while ago going around that said if you change a design by 75% you then owned the copyright, that's simply not true.
This has a good explanation here
Copyright basics for graphic designers – Part 1
Pretty much covers it.