Call your insurance company guys! Ask from the Horses mouth yourself!!! Don’t tell them your real name if your worried...
I can only tell you from personal experience on making sure I’m legal for my time here which is under 3 months a time , on this forum you get all sorts of opinions and some things develop legs of there own and people believe as fact after awhile there always was fight here about 30-90 days rules , 3 yrs ago it developed legs that you legal only 30 days long as your tourist card was valid ... the insurance company I posted up above is from well known respected expat insurance broker website...
The insurance company statement in the website that you posted confirms that the insurer will pay 3rd party liability damages in 99 percent of the cases regardless of whether you are here legally. I think what you are confusing is the follow up statement that says an insurance company may not pay for damages to your own vehicle if you are here illegally. English is obviously not the first language of the author in this website, but here's what it says: "CONCLUSION: Every valid car insurance pays the damage or injury of the third party = liability in case of guiltiness! The Full insurance is not obligated to pay the owners damage, but does it in most cases (99%). Every Insurance provides the Guarantee (Fianza) and a Juristic assistance. The insurance from the other party is not obligated to pay your damage when you are guilty!"