That's a common statement but somewhat inaccurate, as it omits the fact that what most of us think of as Spanish is Castillian, which has a heavy influence from Arabic languages.
Spanish native speaker here. The influence from Arabic is mostly in vocabulary, about 10% of our words have Arabic roots. However, Arabic had negligible influence in structure and grammar. Spanish is your standard Latin derived language.
As a fluent Spanish speaker, I won't go that far, but now that I am learning Latin, I am amazed how easy it seems. As an aside, I can understand ~80% of spoken Portuguese and maybe ~50% of Italian.