That's an interesting one to debate because the wording isn't that clear!
Earlier in that paragraph, it says: or as a part of a "check and relight" procedure following the interruption of the gas supply (e.g. following a gas tightness test) and there is a need to re-establish the gas supply.
When I first read this, like you, I took it to mean that a tightness test was classed as an interruption of the supply. But if you remove some of the extra bits of the sentence, you are left with: or as a part of a "check and relight" procedure following the interruption of the gas supply and there is a need to re-establish the gas supply.
So what they are describing, is "purge and re-light" of which tightness testing is a part of the process. If you look further in Unsafe Sits to the Visual Risk Assessment (Following temporary interruption of gas supply) they give the example of meter exchange which would require purge/re-light + the 6 trigger points.
I had this debate with CORGI back when they were registration holders because I was concerned that our engineers weren't doing flame picture on tenant cookers following a tightness test. They came back with a simple tightness test, without cutting into the supply or removing the meter (introducing air), wasn't considered an interruption of the supply.
They also said that if a tightness test was considered an interruption of supply then any time a customer turned off the ECV or a pre-payment ran out of gas, then the 6 trigger points would be required. Imagine that being requirement!
I do think the way they've worded it is confusing and wish it was worded in a better way. It would also be interesting to hear other engineers' opinions on this.