I agree with this analogy, but I can see other ways of looking at the issue as well. A hashtag, after all, has some flexibility; we can see it in many different ways. And by seeing the hashtag #blacklivesmatter in a slightly different way, I have also come to see the problem with the attempted retort #alllivesmatter in a different way as well.
Imagine the hashtag #blacklivesmatter, not as a plea or as a proposition. Imagine it as a simple statement that we all long ago signed onto. In this light, the hashtag contains an accusation: the lives of Black people matter; you know it, I know it, we all know it, but our society, and particularly our justice system do not act according to our understanding. The power of the #blacklivesmatter hashtag stems from our recognition that our actions and the behaviour of our institutions do not reflect our stated ethics: therefore, #alllivesmatter will always embody a weak response, a feeble denial. Simply acknowledging the phrase "black lives matter" as a statement that calls for a response shows that at some level those who respond understand the problem exists. If black lives matter did not call our attention to a real problem, we would respond with "of course", rather than with "all lives matter".