Yes, there will always be a fee to sell. This will be the case when done through a DRiP or discount broker.
The advice that the financial adviser offered makes sense, but needs to be seen in context.
Let's say that you have $50,000 in MMM and you are retired. Do you sell the entire stake at the same time? Probably not. Despite the fee, it is probably going to be best to sell that $50,000 stake in stages.
Let's turn things around and say that you have a $3,000 position in MMM and you are going to sell. It would almost certainly make sense to just go ahead and sell the whole thing at once. Selling it in (for instance) five stages would really hurt you as far as fees are concerned.
So while the advice you heard might be solid for many people, it may not necessarily be proper in your case.
I have always followed what I call the 1% Rule, which is that no more than 1% should be lost to fees. So if you have made purchases without cost and are looking at a $15 selling fee, your sell should be at least $1,500. Obviously, if you need the money or have realized that the company is a loser then that is a different situation, but I think that the 1% Rule is a fairly good general guideline.