While the following certainly does not authenticate the OP's coin as real - it also doesn't provide any indication the OP's coin is counterfeit.
So you are complaining that the counterfeiters aren't being greedy enough? Cost a dollar apiece or so to make. What are proof silver eagles selling for? $40? $50? If so they could probably sell at least a 3 or 4 thousand to unsuspecting newbies are a bargain price of say $30 each and ONLY make $90 to $120K, and you don't think that is good enough to make going to all that trouble worthwhile.
I'll wager they might have spent more to get the empty mint boxes and COAs than they did on making the counterfeits. The fake coin was growing spots and going bad as I looked at it over the few days I borrowed it for photographing. The thing was really made of ticky-tacky and little else.
They have counterfeited a large number of denominations and varieties, some rare, many common; below is my list. Note all of these had examples in genuine TPG holders:
I have no specific expertise in this denomination, but lighting issues aside the 6 in the OP's coin looks substantially different from the 6 in the Coinfacts examples.
I put together a comparison image of three sold PCGS examples of the same grade and this one for reference:
I think there may be some debris in the upper part of the triangle on the 4. Factoring that out, the rest of the 4 looks reasonably consistent with the others IMO. Can't say the same for the 6.
Could be my eyes, but the date doesn't look like it matches the map very well on the subject example.
The date does look a little thin in comparison to the others and her arm slightly fat. Could just be from die wear though. I’d love to see in hand as it’s a tough call. If it’s a fake it’s a really good one
The resolution for the image of the subject coin is not very high. So I can't say with any level of confidence as to whether the date matches or not. Really need an image with better lighting, contrast and focus.
My friend at the TPG would like to see it in hand- his comment "My first impression is that it is OK, but rather cleaned, and perhaps, somewhat distorted. In hand examination could verify. Thanks for calling our attention to this situation".
The match up on the top left coin...the one in question does not match up.I agree with Mike that the date was the first thing my eyes went to ......and didn't like what I was seeing....it looks off. There's no record of the number of obv. And rev. Dies used to produce the 1864 S h-10. I would estimate that the number of die pairs would be very low.....with the mintage 90,000.
I did check the Steven Crain Collection, and there is only a single example of the 1864-S Half Dime in it, implying that there is indeed just the single die marriage.