Actually, if you are stating so just to avoid this one point, it may be useful for you to know that you don't need to own copyright in order to prevent the situation you've mentioned (ie someone telling others that your works are in fact done by him; which is also sometimes called "false attribution").
The following are well established avenues to combat false attribution:
1. Common Law - Tort of Passing Off
This is applicable in Singapore and affixing his own name on another person's work may give rise to an action of passing off. Normal passing off is affixing someone else's brand on his own goods.
If the bad guy takes the photographer's work and then says "This is mine"; then the well established action of "reverse passing off" may be applicable.
2. Statutory Law - Copyright Act.
Section 188 onwards imposes a duty not to falsely affix another person's name or otherwise imply that another person is the author of the work. This duty is owed to the author and not the copyright owner.
Where S188 has been breached, then the aggrieved person (ie the author) can then file an action in court for damages and an injunction.
These avenues are in fact, perhaps more useful in combating the false attribution of authorship than copyright would; because copyright does not prevent someone from taking a legitimate copy of a work (say a wedding album) and then telling someone else "I did this".
There is no breach of copyright (at least in my mind) to do this. Hence, going by the copyright route will not get the result you want (ie to stop false attribution); and is in fact, the wrong cause of action.
Of course the above is necessarily brief otherwise I may be accused of giving a lecture again, but if you have more questions,I'll be happy to discuss further
Something for you to consider if the false attribution is a problem for you
Hope this is useful