Bicycle fork design history
According to the post the bike display said "circa 1895" so the claim is that it was made around 1895. Is this believable?
I think it is. During this period there was a lot of creativity directed at bicycles and there was a lot of variety in construction methods.

To validate the approximate year on the bike I thought to find another reference for the same bike. Searching for "White Crown Bicycle Company" in a variety of search text strings came up with nothing. 

Next, I looked to find bikes from the period with similar looking construction. During my hunting it was clear that your observation was mostly true.


  All other bikes I've seen from that era appear to use separate pieces for each blade.


Most of the forks in that era were obviously constructed with individual blades and some type of stamped or forged crown.

Here is a picture of an 1892 Iver Johnson No. 1 Diamond Safety Bike with what might be similar construction methods

It's not exactly the same but it's similar and it's very different from the crown with blades fork.

The rear stays seem to have a similar construction

I spent a lot of time reading the article on this bike to try to verify that the fork blades and frame stays are actually tubing and not just bent solid steel. As near as I can tell it really is tubing.

As Criggie said, the fork in the original post may not be a single bent tube.

The fork and rear stay in the pictures I've posted may not be a single bent tube. It could be a rounded crown with blades brazed onto posts and smoothed out to look like a single tube.

My thought is that if the bike below is from 1892 then it's reasonable to think that the bike in the original post is circa 1895.

If you send your picture and information to Colin at The Old Bike Museum he might provide you with better information.