Does NZX have a serious conflict of interest?

Reports have emerged that the company that operates the New Zealand stock exchange, NZX Limited, has initiated a review of its own operating policies and processes—with a particular focus on conflicts of interest (and perceived conflicts). The review is timely, because NZX seems to have begun operating beyond what might be considered reasonable for a market operator. 

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So, what's the problem? Let's start by looking at NZX itself. Here's how NZX describes its business activity:

NZX builds and operates capital, risk and commodity markets and the infrastructure required to support them. We provide high quality information, data and tools to support business decision making. We aim to make a meaningful difference to wealth creation for our shareholders and the individuals, businesses and economies in which we operate.

This seems reasonable. NZX owns infrastructure, operates markets (including regulation) and provides information. However, what is not stated is that NZX also runs a funds management business line. Therein lies the problem (or the perceived problem), because the funds management business invests in companies that are themselves listed on the exchange.

If you'll allow a sporting analogy: NZX sets the rules, provides the playing field, referees the game and is a player as well. Player coaches are common in sport, but player/referees? 

Some might respond by saying this is a great example of the capitalist system in operation. It might be. But I can't help but wonder whether NZX is operating right at the very edge of what might be considered to be ethically and morally reasonable. Consequently, I look forward to reading the results of the review.