That is a possibility. Queen Margrethe intending to wear one of her own but something happened to that particular piece and while in London using a tiara she took from her mother to her niece Alexia. Another option is that she loaned a tiara from her sister and the two of them decided the unknown tiara that was intended for Alexia would be a suitable option. Had she worn one of the Greek tiara's questions might have been asked.
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I guess something happened to Queen Margrethe's own tiara in the last minute - and Princess Alexia's tiara was the nearest one available?