My initial thoughts would be things like the following from current BS7671 wiring regs
134.1.4 Requires joints to be of proper construction as regards to conductance, insulation, mechanical strength and protection.
also 526.1 requires connections to have adequate mechanical strength and protection.
526.3 requires connections to be accessible for inspection, testing & maintenance, unless they are designed to be inaccessible and/or maintenance free with appropriate accessory for terminations..
526.5 requires all terminations and joints to be within a suitable enclosure or accessory.
526.8 requires that cores of cables that the sheath has been removed from shall be within an enclosure as per 526.5
In my opinion PVC tape joints would not comply with any of those...
Nor the good workmanship & proper materials by skilled persons required by regulation 134.1.1
Once the cable had been cut it would have been better to add a new section on cable correctly routed through the joists, (not over the top), then two suitable maintenance free junction boxes at either end of the new section to reconnect the circuit.
(Check-a-trade earn their profits, from the annual membership fees that their contractors have to pay them...
So its not really an un-biased opinion they give...
As they don't really want to bite the hand that feeds and pays for all those expensive TV adverts!)
Is the electrician a member of one of the electrical trades bodies?