These kind of employers really set my teeth on edge!
Basically, unless you get a precontract from this employer, there is no way that you can apply for a work visa (either temporary or permanent).
In order for your employer to give you the precontract, they need to go and register at immigrations as a company that "requires foreign staff" and to do that they need to submit their necessary paperwork from the AFIP (Argentine tax office) and criminal check (if it is a small company). If its a large company, there's various other paperwork they have to submit.
As far as her telling you that they had a French employee that worked for another IT company for a short while and then jumped ship...that is impossible! Work visas for foreigners are TEMPORARY and SPECIFIC to a particular company/sponsor. You have to get it renewed every year for 3 years, after which you can apply for a permanent visa and then jump ship and work for whomever you like under the same terms and conditions as any other Argentine. So the French guy must have been working somewhere else for a considerable period of time (+3 years) before switching companies. If the French guy did get his 1 year visa from another company and then decided to leave within that time period, his previous company is obliged to notify immigrations...and would stop paying his tax and contributions when he left! Either way, even if he got away with that...his visa would run out at the end of the year anyway and it would be up to his current company to start the process of employing him!
As far as getting a CUIL is concerned, I have heard from a couple of people that a foreigner is able to get some kind of tax registration here (so perhaps you could do that). Even so, you would still be working on a tourist visa (illegally!). I think a lot of companies here prefer to "employ" foreigners under the table or, in exceptional cases, have them get a CUIL in order to avoid the hassle and (mostly) the taxes/various contributions they would otherwise have to pay for that foreigner.
To get residency here, you need to have at least a temporary visa...You can either get married, have a child here, obtain an offer of (legal, contracted) employment or apply for a rentista visa (by proving that you have +US$1,000 of external income). If you do not meet any of those requirements, you can't get residency....punto!
As far as I can tell, unless you qualify for one of the above visas (which would still take a while to apply for) there is no legal way for you to accept this job - and it's really shady (though perfectly typical!) of your employer not to give you the precontract. It seems like they're basically just trying to cut costs. There are however, several IT companies here that do employ foreigners legally...and if you're planning on staying here long-term, it might be a good idea to check them out. In fact, the only unmarried, young foreigners that I know who are working here legally, work for IT companies!