Actually, there´s a difference between с любимой собакой and любимый шарф. In the first one, "o" is pronounced not exactly as a stressed "a" in 'чай', it´s kind of a mixture between "a" and "э"(it always happens with unstressed os). In the second one it´s an "ы" and it´s pronounced as an "ы".
The problem is that when we speak fast, we don´t articulate every sound, so probably that´s why you don´t hear this difference.
Russian Language Teacher.