The poster is concerned about how the valleys of his roof are done. He wants galvanized metal bent to fit the valleys of his roof before the shingles are put on. Your link is to a web site about metal roofing. That would include roofs that have metal shingles and "copper roofs" that are typically only installed on the most expensive of homes.
I'm no expert on roofing, but I did act as the "general contractor" when my sister's house needed new shingles. (Basically, the family relied on me to make all the decisions on what to do, and the Bank of Dad paid for it.) That's because it's not really possible to hang around DIY Q&A forums for years and not learn a little bit about everything, including shingle roofs. I haven't responded because I was hoping a roofer would be answering your questions, and a roofing contractor would know vastly more than I.
I think you may be forming an opinion on metal flashing based on insufficient or incorrect information. Where I live, roofing contractors don't use galvanized metal in the valleys hardly at all anymore.
Standard practice years ago was to cover the valley with tar paper, nail your galvanized metal down and shingle up to the valley from both sides, typically leaving a 2 inch gap or so between the shingles. The problem with this system is that if leaves and stuff accumulate in the valley, the compost that forms up there can plug up the valley so that water ends up flowing laterally sideways under the shingles. You have to remember that the galvanized metal is typically only 16 inches wide, and water will flow laterally 8 inches under the shingles. And if the water sits on the tar paper too long, it can start to leak through it.
The other problem with the galvanized valley is that if water gets between the shingles and the galvanized metal, and subsequently freezes, it's going to expand. Since the roof is covered by tarpaper when you shingle, and most roofers use pneumatic nailers, they can neither see what they're nailing into, nor can they get any "feel" from the pneumatic nailer that the nail is driven solidly home like you can from a hammer. So, if it just so happens that they put a nail right into an old nail hole, they have no way of knowing that they've just created a potential roof leak.
If water gets under the shingles there, and expands, it's going to push the shingle up and pull the nail outward a tad. That nail hole will then leak water if water gets under that shingle again.
Nowadays, what they do is put ice and water shield down in the valley first. (I don't know if they put tar paper over the ice and water shield or not, but it's irrelevent to the discussion.) That ice and water shield is a sticky bitumen strip 36 or 42 inches wide, so it extends a lot further from the valley than galvanized metal would. So, the liklihood of water spreading out under the shingles as far as the tar paper is very much less.
Also, the bitumen is a soft material and on a hot day it becomse a very viscous liquid and flows around things like nails to seal off nail holes from leaking water. So, if the same thing happens, the bitumen ice and water shield will seal up around that nail on the next swelteringly hot day to plug that leaking hole.
Basically, if your roofer installed your roof the way it's being done in Winnipeg now, your roof valleys are more waterproof than they would be with galvanized metal in them.
My feeling is that your roofer simply didn't understand why using ice and water shield made for a more waterproof valley than galvanized metal, but was aware that it did. He certainly didn't want to say: "Yeah, but then there's a much better chance your roof will leak." cuz then you'd be losing sleep. But, he was probably aware that they way they're doing it now is better, but didn't understand why.
but I admit they wore me out on their resistance at the very last minute when the roof was scheduled and i neglected this resource...but it is still not too late for negotiations..I have not paid them
Don't go there. You need to know about something called a "builder's lien". If someone does work on your house, and doesn't get paid in full afterward, they can put a lien against your house. That means that if you ever sell your house, the buyer's lawyer will check to see if there are any liens against the house. If so, then the person holding the lien is legally entitled to get paid before you get what's left of the purchase price. So, refusing to pay or haggling with your contractor over price is not a great idea. If you both dig in your heels, and you end up with a lien on your house, then he's gonna get paid eventually anyhow. And, there could be interest accruing on that lien, so it could end up costing you a lot more than it will to pay up now.
Whenever I have a tenant moving out on me because they've bought a house, the chances double that they're gonna skip out on me without paying the last month's rent and not lift a finger to clean before leaving. They think that once they're in their own house, I can't do squat. It's only when they find out I've put a lien on their house that's accumulating interest that they realize I have them over a barrel. Every experienced contractor worth his salt will know his way around the law courts building in your town just like every experienced landlord will.