Both sides are correct. He was very lucky, but he had a pretty good understanding of the types of tactics that would increase his likelihood of success. First off, you should read Matthew Restall's Seven Myths of the Spanish Conquest

So to more directly answer your question. Cortes and most of the men who were with him had experience in conquests in the Caribbean. That meant that they had some understanding of tactics and strategies that would be likely to lead to success. Neither Cortes nor many of his men had formal military training. That said for hundreds of years Spaniard's had been fighting the reconquest against Muslim caliphates and martial knowledge was probably relatively common. Those campaigns as well as the early campaigns in the Caribbean helped prepare the way. Cortes often gets credit for using several strategies that were really pretty common. 1) capturing the leader of your opposition. This was not unique to Cortes and had been used previously in the Caribbean 2) finding your opposition's enemies. Also not particularly unique to Mexico, and an example of his luck. His ability to communicate with the Aztec's enemies was due to not one but two coincidences. First, he found a shipwrecked sailor that had learned Maya and second a Maya leader gave him an Aztec woman who spoke Nahuatl (Aztec) and Maya. So before he even reached the Aztec empire he had the translators he needed to negotiate with Moctezuma or Moctezuma's foes.

That said he was probably a pretty shrewd negotiator and was able to use his ability to negotiate very successfully. In terms of raw men at arms, by the end of the conquest Cortes was 'commanding' several hundred Spaniards and several tens of thousands of native warriors. The willingness of natives to join his side was due to his skill at diplomacy but was more tied to the internal political divisions of the empire than it was his unique genius.

And we should remember there were several moments when native groups could have killed every last Spaniard and did not. The Tlaxcalans debated killing them all. Moctezuma could have ordered their death early on. After Moctezuma died the residents of Tenochtitlan tried to kill them all during the Noche Triste and almost succeeded.

So all in all you cannot separate the military tactics that helped lead to conquest from the more situational factors that facilitated conquest.

/u/historianLA has covered the debate extremely succinctly, so I just thought I'd add my two cents about Cortés. The man was fantastic at improvisation. The entire expedition was an act of treason from the start - Diego Velázquez who was governor of Cuba at the time ordered Cortés not to embark but Cortés did anyway. There are some wonderful stories of an enraged Velázquez standing on the docks shouting at ships leaving into the sunset - certainly apocryphal but entertaining nonetheless. However, Cortés was faced with the issue of retrospectively legalising his actions.

The First Letter of the conquest sent to Charles V was written in the first person plural - "We have reason to believe that..." yet the writer is almost undeniably Cortés alone. The letter was written as the voice of the town of Rica Villa de la Vera Cruz which was founded by the expedition. Cortés was no professional academic but he had a decent knowledge of Castillian law, which allowed towns to appeal directly to the King, circumventing any interference from Governor Velázquez.

Therefore we have a letter widely accepted to have been written by Cortés, pretending to be an entire town of loyal subjects who have come to the conclusion that returning to Cuba as Velázquez had ordered was not in His Majesty's best interests, and that they should push further inland to find more riches and glory for the Crown. However, since their old orders were now invalid, Captain Cortés no longer had any authority, so a leader for this new expedition had to be chosen. Lo and behold, who should be present but that zealous and experienced chap, Hernán Cortés. He is quite literally decommissioned as Captain and recommissioned as chief justice and mayor of Vera Cruz on the same page of a letter that he himself wrote.

Some further smearing of Velázquez as greedy and disloyal later on in the letter seals the deal, and the letter is rounded off with extensive notations on just how many rare and expensive items they have captured to be sent back to the King, and a last appeal from this 'town', begging the King to affirm Cortés' authority and recognise that Velázquez was a bad apple who was only looking out for himself.

As /u/historianLA pointed out, it's a case of six of one, half a dozen of the other as far as the entire conquest is concerned. However, I just wanted to provide further detail on how politically capable Cortés was. I could go on about beaching and stripping the expedition's ships, which made it a case of 'conquer or die' and added the hundred or so sailors to his band of conquistadores, or the fact that he not only defeated the (larger) force under Narváez sent to arrest him but then convinced the defeated soldiers to join his expedition. Certainly, disease, factionalism and Aztec political weakness were important factors, but Cortés himself, whatever faults he may have had, was fantastic at improvisation and a shrewd leader of men.

For more info, I'd suggest Hassig's Mexico and the Spanish Conquest, and second the suggestion of Restall's Seven Myths.

Edit: Cuba not Hispaniola