Pedrosa set the fastest 'laptime' in qualifying for the recent Barcelona MotoGP. The media actually promoted that fact:
Dani Pedrosa took a dominant pole position for the MotoGP race at Barcelona, smashing Casey Stoner's qualifying lap record from 2008 in the process.
His 1m40.893s was nearly 0.3 seconds faster than Stoner's record, which was set when qualifying tyres were still used in MotoGP.
So it seems, perhaps, it depends on the category and how they promote it, as to what's important. For the record, the wiki for the lap record at the same track 'lap record' belongs to:
1:21.670 (Kimi Räikkönen, Ferrari, 2008)
Does having a lap record being beaten equate to being seen as an improvement?