OK. So, if I travel in my car from London to Bristol at an average speed of 60 mph does that imply I travelled at exactly 60mph the whole way?
Of course not, most of the way you would have been going a few mph above or below 60. But if someone phoned you from Bristol and said they wanted you there in 5 minutes, you'd need a faster mode of transport.
In the same way, the rate of accumulation of chalk might oscillate a bit above or below average. But fossilization would need a rate far higher than average - current rates wouldn't be enough.
A catastrophe such as a severe storm, plus a large plankton bloom, could conceivably cause lots of ooze to be deposited into one place, possibly burying small sea creatures - let's say once in every 5,000 years. But that may not fit the picture we get when looking at the chalk cliffs.
The uniformity of the chalk layers suggests to me that they were laid down without big gaps of thousands of years between them.
Also, the global extent of the chalk beds suggests that they were caused by more than local catastrophes.