i agree completely with you about fakes, such as your door example. When I mentioned button head bolts, it was in the context of the things in the following picture from last week:
They're tree guards, which stop my sheep eating my trees, and are both tough and ornamental at the same time. The first batch I made, about 10 years ago, were assembled using cold rivets (which I can buy fairly easily), but the hole tolerances need to be tight, and frankly the assembly is a pain. The ones you can see use M5 button head bolts, with 5.5 mm clearance holes, so the whole assembly becomes trival, especially using a cordless driver. Nuts are clearly visible on the inside of the guard, but there's no doubt the button heads look better than hex heads, and as I said, especially after galvanising, which fills the hex sockets in. I'm not trying to fool anyone, just achieve something which works well, and looks pleasing.
Now you've got me going, my house dates from 1480 +/- 10 years, and has 31 windows. Most of them were replaced in the 1960s, and were in poor condition by 1986. So... I bought unseasoned local oak, gave it 5 years to season, cut it, planed it and put mouldings on, and then assembled new windows which are in the style of 1550, except I used a power tools where possible, and also used modern waterproof glue. I claim they're not fakes, but very practical and beautiful things. I didn't go for the 1480 style, although there are several originals preserved effectively inside the house walls, because it was pre-domestic-glass, and they used thin animal skin for glazing, or left them unglazed and just slid wooden shutters across on the upwind side of the house, and I do like a comfortable house!
Likewise the actual glazing is all of multiple 3" x 5" rectangular panes within the larger apertures, held together with lead strip - over 2,000 of the little brutes, and all cut and soldered together by me, like the originals. However, I used horticultural glass, because it has more defects and colour variation in it than window glass, and to my mind looks interesting; I also used a long-life polysuphide compound for sealing the glass to the lead, because the original stuff used pig fat, red lead and a bit of arsenic, which is 'orrible, and doesn't last very well either. Now the glass and the sealant wouldn't fool any expert for more than seconds, and were used because they work very well, and are available easily and at an affordable price. Are they fakes? Again, I would say no, because the intention is to achieve something which works well primarily, and secondarily looks aesthetically pleasing.
The criterion I mainly use when deciding whether to use modern materials and methods is "would the original maker have used my newer techniques if he had them available"? That isn't the whole story, of course, and in some cases it's appropriate to get materials and use techniques as close as possible to the originals, but not always.