I'm not sure I understand the reference to post-tensioned concrete, but if I'm reading the rest of this correctly, I think you're saying there isn't much load in the diagonal member when there isn't a train running on that portion of the track? If so, I agree. The tension load is caused by the dynamic forces of the train moving along the track, and the diagonal member probably doesn't have much to do when the coaster isn't operating. That being said, from an engineering perspective, that member is very clearly a tension member. That isn't to say it is not also loaded in compression at some point, but I'd be willing to guess the largest force it sees by far is a tensile one. This may not be immediately apparent to the public (there's no reason it would be), but I think most people could understand why with a quick 5-minute lesson.
The diagonal member will be loaded in tension when the train passes just by virtue of the support and track configuration. As shown in the video where the train rides over the failed support, the top-most portion of the support moves to the right since it is no longer attached to the rest of the support. If not for the separation, the diagonal member would resist that rightward movement by pulling the vertical member back into place like a rope or chain, therefore the diagonal member is in tension in that situation. The vertical member, however, is likely modeled as a compression (i.e., pushing) and/or flexural (i.e., bending) member, though. The diagonal member goes into tension when loaded by the train, but tension doesn't have to be put into the support during construction. Referring to your first paragraph, post-tensioning strands (and prestressing strands, for that matter), are installed in concrete for the sake of the concrete, not the steel. Steel does not have to be prestressed or post-tensioned to effectively carry load (most of the time...nor does traditionally reinforced concrete that uses only rebar). The sand just adds extra dead load the diagonal member has to deal with when there is no train- it wouldn't have much of an effect on the member's tensile capacity. But steel, whether a box, tube, angle, wide flange (i.e., an I-shaped beam or column), strand, wire, or cable, can be put into tension by any pulling force applied to the member. The shape doesn't matter as long as the member can be pulled.
I have no idea how often B&M expects the entire structure to be inspected, but I would be very surprised if it's the "daily" inspection some folks are saying "should" happen.
We'll see if I figured out how to use the quote feature with interspersed comments. My apologies if not.