I owned CXs from 1984 up to a couple of years back and still have a couple that "one day" may once again see the light of day and have to agree that they were a rare beast when it came to blow outs/flat tyres; first you knew was when the chunks of black rubber spraying past the drivers window began to get to around shoe sole size and were banging off the underguard area.
It was often said that tyres on a CX were there mainly to stop the rims getting damaged by the road surface and not much else.
However, I have had one instance that gave me a great insight into how well a BX will handle in certain circumstances.
A couple of years ago, I bought a cheap 16Trs from about 400 klms away from where I live. We went down to inspect it with cash in the pocket and bought it on the spot. My son (in his wisdom) then suggested we go another 120klms round trip to get a Pizza he had put great wraps on, so I set off at around 8pm after having settled the business, to get aforesaid Pizza but left the Trs where it was.
Called back and collected the car at about 10pm, we set off home and without going into all the gorey details, we hooked onto the back of an overnight truck that delivers papers all up the coast here and covers about 1000 klms a night and he really flies. To make a long story short, we did one stretch that normally takes about 1 3/4 hours in around 1 1/4 hitting speeds up to 170 kph and sitting around 130 - 150 most of the way.
To put it into perspective, I was a race and rally driver at a reasonably high level many years ago and he currently drives sprints and hillclimbs so we both knew our limitations. I noticed he occasionally fell back on us and I would slow down to let him catch up. When we got home, I asked him how the Trs handled and his response was "fairly good but seemed a bit loose in the back end at times" which caused me to look at the tyres. One was almost dead flat; then it dawned on us. The guy we bought the car off commented on how he had left the spare on the floor of the boot because he had been driving the car with it on as the normal tyre had a slow leak. Idiot didn't tell us he had refitted the tyre with the slow leak without bothering to get it fixed, so our little sojourn down for the Pizza gave it time to deflate.
Moral of the story is that if the flat is on the rear, it's still not easy to pick and it definitely is well above the performance of an ordinary car.
Alan S