Compound lower-body exercises performed through a full range of motion (e.g., squats) induce greater hypertrophy in the distal regions of mono-articular quadriceps muscles (e.g., vastus lateralis) compared to isolation exercises, likely due to training at longer muscle lengths.

Study: Comparison of Muscle Hypertrophy and Strength Adaptations Induced by Back Squat and Leg Extension Resistance Exercises.

Squats made the lower part of the big thigh muscle grow more than leg extensions did, which is exactly what the claim said would happen because squats stretch the muscle more.

Study: Exercise speed and workload effects on muscle hypoxia in vastus lateralis muscle during squatting exercises

This study found that doing squats all the way down (full range of motion) makes the thigh muscle work harder and get more oxygen-deprived, which helps muscles grow — supporting the idea that deep squats are better for building muscle than shallow ones.

Study: Which ROMs Lead to Rome? A Systematic Review of the Effects of Range of Motion on Muscle Hypertrophy

Full squats (full range of motion) make the lower part of your thigh muscles grow more than partial squats, because stretching the muscle more during the exercise helps it grow better in that area.