Contractor not using thin set between sub floor and cement board
This is a subjective question. Here are the factors as I see them:


Hardi apparently doesn't require mortar under its cement board if it's screwed down properly. The guide referenced above seems to be more suggestion than warranty requirement. If the fastener schedule provided is followed closely, problems are not likely to occur. However, a mortared system will be more rigid, potentially reducing tile and grout cracks between floor joists. 
Your subfloor is OSB, so it's questionable whether a mortar bond is wise at all. OSB is widely considered to be unsuitable as a tile substrate due to its tendency to swell and delaminate from moisture, but this is a bit different. It may have worked out with no ill effects. The mortar would serve to prevent any gaps between the layers of the substrate system, improving stability.
Your contract apparently doesn't stipulate mortar in this case. With Hardi's blessing, you probably have no legal standing to insist on mortar. 


In my opinion, you'll probably be satisfied with the results if only screws are used. It's difficult to predict how much floor movement will occur with the information provided. That said, a mortar bond would generally be considered a higher-quality installation. 

In the end, the decision comes down to your willingness to settle for 95% quality or to deal with the dispute between yourself and your contractor.