Hmmm... I don't see any reason why Tesla would lie about their delivery numbers though. Halon's Razor would argue that Tesla's grossly accelerated deliveries in Q4 (end-of-the-year) is leading to errors in IHS Markit's numbers.
Overall, Tesla clearly has a demand-problem demonstrated by Q1 numbers (30% drop in deliveries, even as the company cut prices worldwide and expanded to China + Europe deliveries). But I don't see any reason to distrust the numbers Tesla is giving out.