A healthy relationship between food and exercise?

Stumoo

Obviously myfitnesspal gives us a daily net calorie intake we should have in order to lose weight at a steady rate (well, for most of us. Of course some are trying to maintain or gain weight). And that net calorie intake is the same regardless of whether you sit on the sofa all day, or are active all day. Any physical activity you log lets you eat more calories to get to your net calorie goal.

As an example, today I went for a run that covered nearly 20km (I'm training for a half marathon) and with a little extra activity I did, I pushed my calorie allowance up from 1930 to 3600 calories. And I ate all of them - big burger for lunch and a few beers too. It felt really good, but does present a few questions:

Firstly, what is people's experience of the best way to lose weight when they are mainly doing so by exercise rather than diet? The two options are the one I took above, aim for your calorie goal every day even if it means (yay!) eating whatever the hell you want if you've run hard on hilly terrain for 90 minutes like I did, OR eat as healthily as you can on days like today while upping the intake a bit to fuel/refuel? Option 1 basically allows me to cheat on my diet without going over my calorie allowance. Option 2 builds up a big >800cal deficit today, which I could offset by not being as strict on days when I don't do as much exercise. Opinions please.

Secondly and IMO more importantly, is it healthy to run in order to eat, rather than eating to fuel my runs? I look forward to big exercise days as that's when I can eat burgers, cakes etc without feeling bad about it. Add to this the fact that I have a perfectly healthy BMI and I'm as slim and physically fit as I've been in my adult life, is this a sign that my relationship with food isn't ideal?