EXCLUSIVE

The shoe everyone thinks Hillary Clinton left behind during her medical emergency is NOT her shoe.

Check it out ... Hillary was wearing black flats during the 9/11 ceremony, but the one pictured near the curb is some sort of leopard print.

Witnesses say she stepped out of her shoe as she fell faint and that may be the case ... but the shoe in the pic doesn't fit.

That said, Clinton's campaign is dodging questions about their initial party line ... that she was overheated and dehydrated. They made the statement before video surfaced showing the extent of the problem. Once the video circulated, they disclosed she's battling pneumonia.

Clinton was diagnosed with pneumonia Friday, so her staff knew the root cause of the problem but chose not to initially disclose it. Clinton Campaign Press Secretary Brian Fallon told MSNBC ... the reason they did not disclose the underlying illness is that they were focusing on getting her better.

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The medical emergency did not dampen George Clooney's support for Clinton. George was in D.C.