This sentence is about listening, not about speaking. Я розумію = I understand. If you speak Ukrainian, I will understand.
Я розумію doesn't tell about fluency. Maybe I can speak Ukrainian fluently. Maybe I don't. This sentence is not about fluency, it is about passive understanding.
If you wanted to say you can use Ukrainian actively, you can speak it, you could say «я зна́ю украї́нську» 'I know Ukrainian' or «я розмовля́ю украї́нською» 'I speak Ukrainian'.
People don't always speak simple. But you can always say «Розмовля́йте повільні́ше, будь ла́ска» 'Speak slower, please', or «Повторіть, будь ла́ска» 'Repeat, please'. It's absolutely OK to ask this.
I see, I understood! From the bottom of my heart, I appreciate your teacher-like explanations :) So, "Я розумію" means "I know if I heard Ukrainian (Regardless of fluency)" .
Certainly, it may be hard to say simple if Ukrainian was their mother tongue... "Excuse me" and "Speak slower" are really helpful! Thank you. I'll memorize them :)