Is the reason really matters?
Elon Musk can shill whatever coin he wants. From what I'm thinking, he is too busy with his life that even putting a few seconds to Twitter is difficult so maybe, his Twitter representative plays a role too on that tweet (lol).
Funny aside, just let him shill whatever and whenever he wants. There are lots of traders that are taking advantage of the post-effects of those tweets.
Of course he can, we also have our own rights and choices which cryptocurrency we would like to shill of but the only different was Elon Musk was a popular person, now known as the world's richest man compare to us, which what we are shilling was based on our testimony, our experiences. Maybe some were speculating that Elon Musk are just having fun by shilling DOGE or having fun by using a #DOGE on his tweets but to be honest, this was a big impact to the DOGE market.