I'm not sure I know exactly what you mean - for one thing, it's difficult to define what a "perfectly pronounced" alveolar trill would be, because every language that has the phoneme /r/ realizes the phone [r] in a slightly different way - but I think the answer probably has to do with coarticulation, which refers to the phenomenon in which speech sounds (segments) have their pronunciation / phonetic realization influenced by adjacent segments, as well as the process of transitioning between two different segments. Although we analyze speech as a series of discrete segments, it's certainly a continuum on the surface, and therefore all phones within words are at least somewhat affected by coarticulation.
To return to your specific example, all this means that a person who can pronounce [r] well in isolation may still have trouble pronouncing words containing the sound, because they are unaccustomed to 1) the act of transitioning between [r] and another sound, and 2) the subtle ways that adjacent sounds affect how you pronounce [r].