Ok! So... this is a really interesting question, but not one that is at all easy to answer, because historians do not fully agree on the subject. A difficulty this raises is that while I am a historian of the Spanish Civil War, I am not a specialist in pre-civil war politics and elections. I am not well-placed, in other words, to adjudicate this debate decisively. I can give you my own opinion, but you should not take this opinion as the sole definitive answer to this question.

As you note, the civil war is still difficult to teach and discuss in Spain, but in many ways the same is true overseas. There is still a great deal of ideological disagreement that defines (often quite acrimonious) historical debate, particularly surrounding the legitimacy of the Republic as a democratic entity. The main difference I would say is that the debate is somewhat more even in Spain (in that conservative voices are relatively prominent), but overseas more left-wing perspectives are still generally dominant.

An exception to the rule is Stanley Payne, who is probably the most prominent foreign Hispanist to align broadly with the contemporary Spanish right. While it is probably too far to say that he sympathises with Franco directly, he is critical of the Republic both during and prior to the civil war. This on one level is fair enough - the Republic was far from perfect, and had been mythologised on the left due to the symbolic resonance of the civil war and the manner of its defeat. However, in attacking the underlying legitimacy of the Republican system, Payne and others echo Francoist propaganda justifying the uprising - particularly the claims that a) the foundation of the Republic in 1931 was illegal and therefore the whole system was illegitimate and b) that in any case, the leftist victory in February 1936 was fraudulent. As such, these kind of historical narratives meet with a great deal of resistance from more left-wing historians, who see it as an attempt to rehabilitate Francoist ideology.

So, this is the context to why the debate is so acrimonious. What can we say about the actual election itself in Payne and other historians' work? What interests me greatly is that Payne's views here have developed significantly in his later work. If we look at his 2006 book The Collapse of the Spanish Republic, he writes:

Conditions for the balloting on 16 February were good, and the elections were generally free and fair. The only areas where there was noteworthy evidence of corruption or coercion were parts of Galicia (subject to manipulation by the government and in La Coruña by left Republicans) and in Granada, where balloting in some rural districts was forcibly dominated by the right. Early returns from urban districts indicated a stronger showing by the left than many had anticipated, partly because of electoral support from anarchists, and by the late evening it was clear that the Popular Front was winning, though the dimensions of the victory were not yet clear (pp. 174-5).

This was more or less the generally accepted line 10 or 15 years ago, and Payne’s description here would be unremarkable in any English-language publication at the time. The elections were as fair as could be expected in the circumstances, and problematic practices were regionally isolated, favoured both sides to some extent, and were not central to the overall result. While the Popular Front victory was disproportionate in terms of seats compared to the margins of the popular vote, this reflected both the Spanish electoral system and that the leftist bloc had cooperated much more effectively than the right (factors which had worked in the right’s favour in 1933). This isn’t the last work on the subject of fraud or fairness, as I’ll discuss below, but indicates that Payne was occupying the middle ground on the issue until quite recently.

Fast forward to 2012, and the book you’re likely referring to, The Spanish Civil War, and Payne’s views have shifted considerably. Instead of the above, he writes:

Balloting took place on February 16, 1936, at first in an orderly manner. By the evening, however, leftist crowds had taken to the streets in a considerable number of provincial capitals and other cities, interfering with the remainder of the balloting and registry of votes in at least twelve provinces. Claiming victory, in several cities they broke into prisons and freed revolutionaries still in jail. In a number of electoral districts, leftist mobs either put an end to voting or destroyed the results of the balloting, which led to the repetition of voting in these areas between February 17 and February 19. In such cases rightist representatives either resigned from the boards conducting or verifying the results or were forced out, and these repeat elections were swept overwhelmingly by the Popular Front (p. 32).

Mob actions and disorders altered the results in at least twelve provinces, producing at least thirty seats in favor of the Popular Front, which made possible the parliamentary majority (p. 33).

The final margin in favor of the Popular Front was primarily the result of violence, mob action, and political manipulations that took place between February 16 and March 1 (p. 34).

This is a much more controversial assessment, directly contradicting his own earlier work, and leads to Payne’s eventual conclusion that Spanish parliamentary democracy had effectively died by the spring of 1936, before the military uprising took place. Payne explains this shift (indirectly – he doesn’t really acknowledge his older position in text) by reference to a new wave of Spanish scholarship, notably from Roberto Villa García, described as the ‘leading student of the Republican elections.’ Villa García is a conservative Spanish historian who is critical of the Republican political culture, with some links to the Partido Popular, though this does not of course invalidate his scholarship.