It was indeed a lie, as anyone would expect, except very liberal gullible people.
https://www.amazon.com/Myth-Andalusian-Paradise-Christians-M...
>From 1510 onwards, any Romani found in Switzerland were to be executed; while in England (beginning in 1554) and Denmark (beginning of 1589) any Romani which did not leave within a month were to be executed. Portugal began deportations of Romanis to its colonies in 1538.
Compared to getting executed for being at the the wrong place at the wrong time with the wrong ethnicity, Andalus may well have been a oasis of tolerance in Europe, relatively speaking.
Al-Andalus (Muslim Spain) is considered religiously tolerant by modern historians in the context of the experience of Jewish citizens, especially when compared to contemporary parts of Western Europe.
As an example, it seems there was an expulsion of around 100,000 Jews in Christian France in 1306 and in England in 1290 of several thousand. I've not come across any such comparable events in my readings of Al-Andalus.
As a direct point, if Maimonides thought that France and so on would have offered more freedom or a better quality of life, then he could have moved there when Cordoba was experiencing political turmoil. He instead migrated through the Maghreb, towards the Middle East - it seems he was employed by Saladin at some point.
I have to find the letter (possibly a Jewish reader can dig it out?) but I remember reading and being amused by a letter penned by Maimonides to iirc Jews in Arabian peninsula. Apparently they had written to him having heard of the paradise of tolerance in Muslim Spain and his letter poo pooing it, telling them it’s no better than their locale. I always read that letter as a sort of rabbinical wisdom on his part: he knew they wouldn’t be able to get there so he painted a dismal picture.
https://en.wikipedia.org/wiki/Maimonides