They were laughed out of court, actually, to an extent.

On the one hand, there wasn't a deception in the sense of what happens in, say, A Knight's Tale - someone faking documentation to make a commoner appear to have a title. It's probable that they descended from Gruntram/Grontran the Rich (920-973), a nobleman in Lower Alsace, via his son Lanzelin; Lanzelin's great-grandson originated the title "Count of Habsburg" in 1090, and they went on from there as well-documented aristocrats. Despite gaining power, the Habsburgs were hampered by a lack of ancestral links to the Hohenstaufen or Salian families - the latter ruled the Holy Roman Empire in the eleventh century and the former in the twelfth and early thirteenth. It made their history shallow, so to speak, in comparison, and gave them no claims to any rulership above the level of "count". So the legend that they were descended from Caesar via the counts of Tuscany and the Colonna family of Rome was very handy for them, when it first came up in the early thirteenth century! And we don't know how deliberate the invention of this link was - a straight lie that was bought by later descendants, or some weak reasoning that led the originator to think it was likely. In the fifteenth century, links to the Aniciana family of Rome and the Pierleoni (who were related to popes and saints), as well as the Merovingians and Carolingians, are in the same hazy category or "useful legends".

(Mythical origins without real documentation were also fairly common at the time, and nothing that anybody would or could really complain about. The skaldic Ynglingatal declared the royal Ynglinga family to be descendants of Freyr; the houses of Luxembourg and Plantagenet claimed to be descended from the mermaid Melusine - and in all of these cases, there was certainly no documentation, since they're entirely mythical! And these were far from unique examples. Julius Caesar's own family claimed descent from Aeneas of Troy.)

But the Privilegium Maius was a true forgery made for Duke Rudolf of Austria in 1359: fake deeds from their supposed ancestor, Julius Casear, as well as Nero and the Holy Roman Emperor Friedrich Barbarossa that gave the family the right to be archdukes, to have various other real and ceremonial titles, and to have a permanent exemption from certain requirements of vassals in the empire (attending imperial diets, giving military aid when requested, etc.). All of this would put the Habsburgs on the same level as the prince-electors who determined the next emperor, which was important because the Holy Roman Emperor Charles IV, Rudolf's father-in-law, had just reorganized the system and left the Habsburgs out as electors. Charles had the Italian scholar Petrarch look the documents over, and Petrarch declared them to be clear fakes, because ... I mean, it was obvious that Rudolf hadn't just happened to find these extraordinary deeds at the perfect time. Charles denied him the rights he claimed, and the Privilegium Maius wasn't actually ratified until 1452, when Friedrich of Austria - a Habsburg - became Holy Roman Emperor. He was able to do it without being laughed out of court because he was the highest power in the land.

What Rudolf did in 1359 was to set up the idea that the family should have rights in the empire on the same level as kings, and to detail the many rights that they should have inside their own borders, creating a real notion of a powerful House of Habsburg. It didn't matter to later generations that his standards only came into being in the fourteenth century: they were useful standards and they wanted to have them.

Jean Berenger, A History of the Habsburg Empire: 1273-1700 (Fayard, 1990; repub. Routledge, 2014)

Benjamin Curtis, The Habsburgs: The History of a Dynasty (Bloomsbury Publishing, 2013)