Apart from (and also emphasising) what others have already mentioned: American English (AE) is a rhotic English accent, essentially meaning that the letter 'r' is pronounced when it occurs at the end of a syllable (whereas with many British English or Southern hemisphere accents it isn't).

The Dutch 'r' phoneme sounds similar to the AE one. Hence, Dutch English speakers will naturally sound more American even if they don't have an actual American accent (which might indeed very well be the case due to said influence from American TV shows).