Frilly this isn't any kind of moral judgement but a practical one. Once you have lied, for the rest of the time you are with that organisation, working with those people, you have to remember that lie. If you ever slip up then the level of the lie wont matter, you will have lied. The organisation might tell the agency that they are firing you because you lied and that is then your rep with the agency ruined as well. IMO Its just not worth it. The Op is in this position through no fault of her own and IMO her picky boss will be just as likely or unlikely to be annoyed about the situation if she said she got coffee spilled on her than if she told the truth....more so maybe because if i was heading for an important meeting with a client, i wouldn't risk getting coffee spilled on me!
It wasn't me who raised the issue of being sacked, it was the OP.