First, some background: the stock rear fender has two creases in it. The fender's outward angle terminates in a first crease (now the metal is going straight downward instead of angling outward) then a second crease (where it bends from going down to going inboard).
/ / . '.' = first crease | L___ 'L' = second crease
I know of three ways to flare the rear fenders:
1. Hammer inward, bending the metal at the first crease so that it goes back in against itself instead of down then in:
/ /./ ('.' = second crease) // v ('v' = first crease)
2. Hammer outward, straightening out the first crease so that there's a straight line angling outward through what used to be the first crease, then hammer the second crease back in on itself:
/ .// ('.' = first crease) // v ('v' = second crease)
3. Cut off the whole fender, move it out and up from where it used to be, and do a lot of bodywork to get it to look okay.
I did (1). I first tried to do (2), but I couldn't get the first crease flat and I really made a mess of the first fender trying before I finally gave up. If you can get it right, it can look okay (I've seen a car which had the fenders flared in this way, which looked fine; I think the difference between that car and mine is that mine has a lot of rust- prevention goop inside the creases of the fenders which was impossible to remove completely and which got in the way while I was hammering. The car I saw where this worked was a '74 and didn't seem to have any undercoating).
(3) is clearly the best option for clearance (and in answer to the question in your subject line, no, it doesn't seem to hurt structural rigidity of the car -- Bill Condrashoff's rear fenders are flared like this, and that car must see harder autox use than any other X1/9 in the country, and doesn't seem to have been slowed down any by the fender work ...), but it requires a real bodywork expert, which I'm not, and I couldn't find any body shop willing to undertake such an ambitious task. (I'm sure I could have found one had I looked harder and been willing to pay several thousand dollars just for the flaring alone, but no one was willing to do it in the under-$500 range.)
The only real trick to option (1) is that you do have to cut slits into the fender below the first crease, because you can't stretch the metal enough to get it to fold back upon itself. I did this with a Dremel tool and a whole lot of cutting bits and some patience (the rear fenders are a double layer, so you're cutting through two thicknesses of sheet metal). This cutting won't be necessary with option (2).
Warning: with option (1) I couldn't get quite as much clearance as I'd like. I get a lot of tire rub on the outside edges of my 215/50-13 tires when they're mounted on 7" rims; I suspect that this will prevent me from using these tires on 8.5" or 9" rims at all (since wider rims offset the tire farther out), but I'll be testing that this week. I would assume that option (2) is no better as far as clearance.