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I think you're looking at different measurements and treating them the same.
The sign is a road sign, and will give the worst incline not the average. It is there to signal to drivers (in vehicles that may struggle) which is the worst incline so that they know whether they are likely to make it up.
The 9% on the TdF stages is the average incline over the given section, not the maximum within the section.
So a 9% on a road sign here is max, and 9% on the TdF profile is average.
It is steeper overall, for longer, long enough to be the average rather than peak incline.
At least, that's the way I understand it.
Velocio
bluebikerider
The 9% I'm thinking of are the two 3 milers that lead up to my village on the top. And there's a sign that says its 13% which according to RWGPS and BikeHike is wrong.
No matter which angle I look at either hill, they just don't look anywhere as steep as they do on The TdF.