Whether the belongings were 'in the room' or 'left in the room' doesn't matter. Where you were doesn't matter. I don't think anyone here can tell you what the precise hotel liability situation is in Bogota. That will be a case of (i) the hotel's policies, (ii) the agreement the operator has with Hilton (if any), and (iii) the country-specific legislation.
I get the impression that the hotel is rather indifferent to this issue, which tells me that there is either no requirement or specific laws. Perhaps the hotel has a policy of very limited liability for guests belongings, as with the Montreal Convention for airlines. That your shoes cost $500 will not be a concern for the hotel. Now, they may do right by you, but equally they may tell you to pound sand. This is why I would run it through travel insurance first, then home insurance.