In the absence of empiric evidence, we can still examine the incentives behind a behaviour (which we have done), and evaluate the sincerity of a statement. Microsoft have more incentive to not be entirely truthful about their server costs (good PR), than they have in giving away their server farms for free when end-users can play the same game on a competing platform anyway (bad finance). Unless there is a clause that they didn't tell you about.
That's a pretty pointless exercise though, as it simply relies on a load more unknowns. We can only view the situation from the point of a consumer, with no knowledge how MS weighs the pros and cons of the decision. Even then I already stated how the free X1 servers essentially only equates to a discount for multiplatform games due to every other platform requiring payment... and selling available server resources at a discounted price is still preferable to not selling it, and having it sit there idle. So there is a reasonable incentive that they may have to offer the servers outside of exclusive arrangements. It's not bad finance if any time a user plays that game on a competing platform it ends up getting you paid. That is a far better alternative to them playing on that platform and you seeing nothing. This is why Office is on iPad, despite the fact that they would prefer you to use it on a Surface (where it is offered free). So they can actually obtain good PR, whilst also attracting additional business (good finance) at the same time.
But you're much happier to simply assume everything they say is lies.