Apparently the peloton was moving quite quickly at the time,
Yes, as a result of having just passed through the first major selection of the race in the Trouee d'Arenberg sector. It was a quite loosely grouped peleton which was just about ready to properly split, with the teams of the top contenders pushing very hard to try and ride away from those riders who had problems in the forest.
If the crossing hadn't closed on the peleton to break up the group (or if the commissaires had not neutralised the front half until those delayed could rejoin after the train passed) then I think Wiggins would have been done for the day at that point. Thanks to the neutralisation, he got a free pass to rejoin without having to burn a lot of energy he would have needed for the final parts of the race.
I'm not sure about how the speed was translated into mph, but that is pretty fast by bicycle standards...
Speeds of over 60km/h (where the BBC got 37mph from) is quite normal for a peleton on flat roads with a couple of teams using lots of firepower to try and chase down a break, split a peleton or lead out a sprint.
If you're in a group where someone else has their nose in the wind, it's actually quite easy for the slipstream to suck you along at 40+ km/h almost without turning a pedal. Add in a bit of a tailwind and you can literally be coasting at 50+ km/h despite being on the flat.
... and I would dare to say that pedal bikes often won't stop as quickly as motor vehicles, especially when there is a risk of going "over the handlebars".
Yes, bikes have a longer stopping distance than cars, but it's all to do with the small contact patch hitting the road rather than the risk of going over the handlebars. The 'over the handlebars' issue is easily prevented by simply having a bike that fits right, sitting in the right position and having good bike handling skills.
It wouldn't be as good as a panic stop in a car, but if you asked a pro cyclist such as Peter Sagan or Zdenek Stybar to show you their hardest stop on a flat road (i.e. not cobbles) I think you'd be quite surprised at how good it could be. The hardest possible stop you can do on a road bike is with the front brake only, applied just hard enough that almost all the weight is transferred to the front wheel and the rear is just lifting off the ground.
To find this perfect level of control to lift the rear wheel requires lots of skill, experience and massive brass ones between the legs. The skill part will be getting a touch easier in the near future as hydraulic-actuated disc brakes become legal for racing later this year. Hydraulic actuation allows for better control (some riders prefer it for even their conventional rim brakes - Mark Cavendish is one) and using discs removes the problem of wheel rims heating up and melting the glue used to hold on the tubular tyres.
But back to the Paris-Roubaix level crossing incident - the problem was not the braking distances or the quality of the road, but the problem of stopping a peleton at very short notice. These riders aren't just a group of mates out for a casual ride, they are elite athletes racing at the very highest level on roads that they understand have been closed specifically to facilitate the event so they can take liberties they couldn't on a normal day when the roads are open. It's no different to what a F1 driver expects when they roll out of the pits and join the track.
A solution needs to be found that would allow the riders to approach the crossing with confidence - either holding the train for a few minutes at its previous stop or an orderly stopping/neutralisation of the race before getting to the crossing (and the restoration of time gaps) would work, just so long as there's some joined-up thinking between the race organisers, governments and rail operator/s. It's not hard - we manage to do it for the Tour Down Under in Adelaide every year despite our race being some 96 editions younger than Paris-Roubaix.
please get real