The famous Victorian rake Alexander Meyrick Broadley was accused of 'homosexual offences' whilst in India in 1872. Would this necessarily imply sexual contact with another white male, or would an accusation from or concerning an Indian male be penalised in this way?

I don't know enough about the details of Broadley's case to give an answer specific to his sitaution, but I'd be happy to tell you a bit about how race and sex between men worked under the Raj. The general working of the race/sex/class/power/colonialism complex in British India leads me to this tl;dr:

Complaints like those against Broadley would most likely have been generated by sex between European men, but not necessarily**.**

Your question implies a few observations that are absolutely correct; first, that the sexual rules were different for people in India depending on their relationship to the Raj (i.e., are you British-and-white, or not). Complicating the seemingly simple "Are you British? Y/N" question were factors like social status, class, religion, skin tone, language, caste, etc.

The second thing that you're right about is that India could be a relatively nice place for British men to have sex with men. Sex between men was only decriminalized in Britain itself in 1967, and the late 19th century was a time when British anxieties about men having sex with men were reaching a fever pitch. Broadley's India case was a few years before a series of scandals* in the 1880s and 1890s leading to and in the wake of the 1885 passing of the Labouchere Amendment, which criminalized not only sex between men, but any act of "gross indecency," even in private. In short, it was not necessarily fun to be a man looking for sex with men in Britain. It was easier to find such relationships in the colonies. Naturally, Broadley wasn't the only British man to have taken advantage of the relatively relaxed attitudes toward male/male sex in the Empire. (The Aldrich source listed below is just, like, 400 pages of British guys loving and having sex with guys in the colonies.)

So your premise is sound: India was a good place for sex, and the rules for sex in India were different for British men and "native" men. So why was Broadley's case most likely involving sex with another European? Two reasons: First, because the Raj generally took the complaints of Britons more seriously than those of colonized Indians. (This was because of the obvious power imbalance between colonizer and colonized.) For a "native's" complaint against a man like Broadley to be taken seriously, they would have needed to hold unusually high political status. Perhaps if Broadley was sleeping with princes, such a thing would be worth worrying about. Alternatively, if Broadley had displayed a pattern of egregious sexual violence against colonized men, it might have risen to the level of A Problem™.

Second, because the sexual behavior of British colonizers was much more heavily policed than that of the colonized. Because twice the white people were involved, there was essentially twice the surveillance being applied to the relationship.

Ann Stoler uses the concept of "white prestige" to explain phenomena like this second reason. Basically, the colonizers need to maintain an image of upstanding moral authority in order to keep their political power. Such upstanding moral authority would forbid male/male sex. Under this rubric of white prestive, sex between male colonizer and male colonized would be taboo, of course. But sex between two colonizers--two presumed paragons of White Civilization--would be even worse. "Sure, those indolent, sensual Orientals are into sodomy, and they might even seduce a fine young colonizer; that's what they do," would go the reasoning. But a white man behaving in that way would mean a dangerous loss of white prestige.

It's not, therefore, that Broadley couldn't have been caught having sex with an Indian man. It's just less likely that such an event would be reported and seen as a problem. If it was taken seriously, it would probably have been because the "native" man involved was either coerced via physical violence, or had an unusual amount of political power.

*One of these scandals was the 1889 Cleveland Street Scandal, in which Broadley himself was implicated.