The way I heard the phrase is "as long as you get the beginning and ending right - what happens in the middle doesn't matter". This is usually used in reference to a whole song.
I would say that some of the theory that explains how this concept relates to a whole song would also apply to a solo in the middle of a song. I am not aware of any controlled clinical studies to prove or disprove it. So any answer would be educated speculation. Here is mine.
The beginning triggers prior knowledge and recognition in the case of a cover song and lets the listener know what song is coming and if they want to listen. In case of an original - or song the audience has never heard, the beginning is where they will subconsciously decide if the song is something they actually want to listen to.
The ending of a known song is memorable in many ways. Most folks remember how a song ends because most songs set up musical expectations and resolve back to home (the tonic) and the endings are well anticipated and sometimes dramatic. They provide a sense of resolution which will not occur if you end on the wrong note or the wrong chord.
The same applies to a solo. The beginning establishes the starting point and should transition smoothly from the end of the preceding section of music. Often it will establish the key or tonicize the lead run melody. The beginning will set up an expectation for a satisfying resolution back to the tonic established by the preceding section of music as well as the beginning of the lick.
Ending on the wrong note (that the audience was not expecting) would leave them hanging. Some well known pieces may end on an unexpected note as a signatory element of the song. In that case the ending would be memorable for its lack of resolution and therefore would set a particular expectation and the audience will notice if you miss the anticipated note.
It has been observed that the beginning and endings of lectures, speeches and even movies are more memorable than what happens in between. That is probably because the beginning is where our brains tune it to determine our level of interest and try to predict what the movie, lecture, play, speech, etc. will be about (and if we are interested in continuing to watch/listen).
The ending is always anticipated and thought about continually throughout the middle of the song, movie, speech, etc. If you are watching a movie or reading a novel you are constantly thinking to yourself "I wonder how this is going to end". And the main reason you keep reading the book, watching the movie or even listening to the song is so you can discover how it ends. That's why if someone starts to tell you about a movie you will probably say "don't tell me how it ends" - because if you know how it ends - you have no interest in watching the middle.
I imagine music is much like any of the other things that have a beginning, a middle and an end. And for many of the same reasons, it's the beginning and ending that are most important to the consumer of the presentation - be it song or verse.