HR doesn't care about your CV. Or almost never cares. The only parts that might matter are things related to specific job requirements, because if you later have an issue they can rely on those to fire you (if you didn't meet requirements) or to cover themselves. This might apply to education - e.g., if a job requires a 4-year degree then your CV showing that is at least proof that you claim it, though the ultimate proof is an official transcript or similar document from an educational institution. Other items might include security clearance (hopefully those actually are checked by HR before hiring), legal right to work in a particular location or job (citizenship or appropriate visa) and similar things.
But your job history? Not relevant at all in most cases. Even if a job posting says "5 or more years of industry experience", that is usually not a strict requirement but rather a way to find experienced people. Using that example, sometimes personal study and projects can substitute for paid job experience and an above average employee can get 5 years worth of "ordinary" experience in 2 years of a high-pressure, high-achievement job.
All the more so in your specific case. They hired you based on your experience up to the interview. Except if you were fired because of wrongdoing, what you did between the interview and when you started work is of no consequence. If you were fired due to problems outside your control - e.g., the company closed a division and let lots of people go, and interns would be the first to go - that wouldn't be an issue. Certainly moving up from intern to full-time would be a plus - but not a problem if not reported.