As far as I can tell, the use of 囉 is by no means limited to "insincere expression". It is just a particle put at the end of a sentence for
emphasis purpose. It is usually used in a reply which may be
contrary to the interlocutor's expectation.
For example:
- 做咗囉! (I have done it already!)
- 得囉! (It works!)
In example 1, the interlocutor may think that the speaker has not done the job, but then the speaker emphasizes that he has done it already. Same for example 2.
In your own example, the interlocutor may not expect the speaker to say sorry, but then the speaker ended up saying sorry, in a rather reluctant way though.