Will my non-compete interfere with my potential new position?

I work for a consulting firm that services a wide range of clients ranging from small imaging centers to large regional medical centers. We have a non-compete agreement that is pretty standard. One of our clients posted an opening for an in-house position, meaning you would work only at the main hospital and some of their smaller satellites. However, this hospital’s satellite campuses are serviced by my current company and they have an on-going contract for some services to be provided. The hospital position was publicly posted and is available for all public to apply, so this position will be filled regardless. The manager at this hospital is concerned that my non-compete may cause a conflict. My take on this matter is that the non-compete does not matter since the hospital position would not be directly competing with my current employer as it is an in-house position only (meaning that you work only directly for that one hospital system).