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I think the key thing here is that the participants were told what treatment they would be receiving. This is in line with an open-labeled clinical trial. Open-labeled clinical trials can still be randomized and do not need a control (as in this case).
divalent cations interfere with the absorption of tetracyclines, not fluoroquinolones.
anti-acids interfere with the absorption of fluoroquinolones. (like in this q, it's ca carbonate)
According to SketchyPharm, divalent cations also interfere with the absorption of fluoroquinolones