A factura is only issued by Mexican companies to show the status of sales tax paid and collected. Mexico is one of the few countries where tax evasion is an open process – most merchants only file their factura (which you NEED to request) with the government when paying their taxes, and their regular tickets of sale for their own personal number (not that anyone there ever cheats on their taxes).
Purchases made outside of Mexico, including property that isn’t going to remain in Mexico, won’t have a factura because you won’t be paying taxes on them. So I think the officer might have been wrong when he requested a factura for your lost personal item, since it’s not taxable. Mexico’s police force isn’t, let’s say…consistently trained as in the US, so there’s a very good chance that he’s never dealt with these circumstances before and if you were in a non-touristy spot the whole station may have never dealt with it. He should have listed it as personal property, not property registered to a Mexican company.
What did your work say? If it’s strictly a financial loss it most likely is covered by your travel/car/homeowners insurance. Some countries require an Letter of Authorization (LOA), but that’s usually only in circumstances where your electronic equipment is registered to make sure you leave with it (North Korea and Cuba for instance).
Fortunately, I never faced a situation where the company owned laptop was stolen, while I was traveling overseas with it, I was given a Letter of Authorization (LOA) certifying that the laptop, I am carrying with me, is a company owned property, for business use, by the Immigration department of my company.
The primary usage of this LOA mentioned to me, by the immigration department folks, was for producing a documentary evidence to the Custom officials, if asked for by them.
The LOA, I carried looked similar to the one posted here.
IMO, the same letter could have been used to assert that the stolen laptop in your case, was a company owned device, and not a personal device. Though, I do not know of any such provision/restriction in law, which prohibits from filing a theft complaint either in USA (based on the answers on this question to my immigration department, when I was traveling to USA) or in India (I live in India).
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