While I don’t know of specific evidence indicating that Caravaggio’s behavior was tolerated because of his artistic skill there is certainly a long tradition of artists getting away with behavior that was outside the norm (or downright illegal/dangerous) and still finding work and favor with patrons. This goes back at least as far as the Middle Ages, and there is evidence that artists enjoyed a status that was distinct from that of other craftsmen (thus allowing them to skirt the law). Defining things like "temperament" and "status" and how artists’ skill or temperament was viewed is challenging. But I’d argue that artistic mastery and expertise were appreciated, to varying degrees, starting at least by the Middle Ages (a few hundred years prior to Caravaggio’s time); that in every period a few artists were always praised and given special treatment; that artists were long cognizant of and confident in their creative abilities; and that they were always, to some extent, marginal figures (who could often get away with "aberrant" behavior).

A lot of this depended on where an artist worked (and for whom). In Italy (and elsewhere) artists could benefit from being established as a court artist rather than working within a guild in a city. Working for a princely court meant a steady income and closeness to court culture, which could almost guarantee an artist was elevated from being thought of as a "mere" craftsman (manual labor had some negative connotations). As an example, in 1426 Siena Cathedral authorities asked the sculptor Jacopo della Quercia to convince a contemporary, Giovanni da Siena, to return from Ferrara (a court city) to Siena; Jacopo responded by describing the benefits Giovanni enjoyed as court architect, which included a salary of 300 ducats a year (very good pay), board for eight people, and recognition as an "inventor" rather than a craftsman. Over a century later, in 1537, the sculptor Benvenuto Cellini requested a pair of horses from the court of King Francis I so that he and a servant could ride to Paris; when representatives of the king questioned his demand for this mode of travel the artist responded by saying "that it was customary for the sons of his art." (Warnke 1993, 125)

Intellectuals also (occasionally) considered artists to be distinct from "regular" craftsman. The humanist author Bartolomeo Fazio, in his De viris illustribus of 1456, associated the class of painters and sculptors with Poets, Orators, Lawyers, Physicians, Captains, and Princes—a much more distinguished group of professions and citizens.

There’s also a tradition of artists receiving special permission and treatment despite their transgressions. In 1281, when Sienese authorities sought the best artists for work on their cathedral, they submitted a request that the sculptor Ramo di Paganello's citizenship be reinstated, after he had been expelled for adultery. The request was granted, no doubt aided by the claim that he was one of the greatest living sculptors in the world (de bonis intalliatoribus, et sculptoribus et subtilioribus de mundo qui inveniri possit, per documents). Jumping forward a few centuries, the sculptor Benvenuto Cellini has a staggering rap sheet: banished from Florence (or flees) in 1516 for seriously wounding two men while defending his brother in a brawl; prosecuted for sodomy and forced to flee Rome in 1523 after another brawl; kills a man in the 1530s (who had killed his brother); attacks a notary in 1532 and forced to flee Naples; murders a rival in 1534; accused of theft from the pope and imprisoned in 1538; accused of theft again in 1545 and forced to leave France; accused of sodomy in Florence; imprisoned for hitting another goldsmith on the head in 1556; accused of sodomy in 1557 and fined and imprisoned [NB: accusations of sodomy could be an easy way of attacking/slandering someone, so we should take all those accusations with a critical eye].

Cellini himself offers us most (all?) of his confessions in his autobiography, although he also suggests that (among other reasons) he should not be judged due to his artist talent. According to Cellini, Pope Paul III says “men who are unique in their profession, like Benvenuto, should not be subject to the law.” (But that's Cellini reporting it, so a grain of salt is needed...)

Finally, by the Renaissance (if not earlier) there was an idea that "melancholy" or the melancholic temperament were associated with artists and artistic temperaments. The Italian scholar Marsilio Ficino, for example, writing in the 15th century, described melancholy as a mark of a great man. This period sees a codification of the notion that artists are divinely inspired geniuses, born under the sign of Saturn (and thus subject to melancholy). Michelangelo is actually called "divine" in his own lifetime (and was famously morose and melancholic). One way to understand Dürer’s print Melencolia I is through this lens: as a portrait of artists and creativity and a sort of “spiritual” self-portrait of the artist himself, who warned his own pupils of the dangers of melancholy. But—melancholy could be debilitating, leading to sloth, despair, inactivity, and insanity, making it the most feared of the humors. But it was also an element of divinely-inspired genius, so there were pros and cons...

In short, there is a long precedent of recognizing artists (painters and sculptors) as somehow "distinct" from other craftsmen, although it's worth noting that we are most likely talking about exceptions rather than rules. For every artist whose name comes down to us and is popularly known there were hundreds of others working in relative or total anonymity, who likely had to contend with laws and norms just like any other working-class citizen.

Some sources for more information (and from which some of this is drawn) include:

Michael Baxandall, Giotto and the Orators (London: Oxford University Press, 1971)

Stephen J. Campbell, ed, Artists at Court: Image-Making and Identity, 1300 – 1550 (Boston: Isabella Stewart Gardner Museum, 2004).

Gaetano Milanesi, Documenti per la storia dell’arte senese (Siena, Onorato Porri, 1854-56; reprinted 1969, Davaco Publishers, Holland), 3 vols, vol I, no 14, p 157. Also see John White, Art and Architecture in Italy 1250 to 1400 (Middlesex, UK: Penguin, 1987 ed), 121

Martin Warnke, Hofkünstler: zur Vorgeschichte des modernen Künstlers (Köln: DuMont, 1985); published in English as The Court Artist: On the Ancestry of the Modern Artist, trans. David McLintock (Cambridge: Cambridge University Press, 1993).

Rudolf and Margot Wittkower, Born Under Saturn: The Character and Conduct of Artists (1963)