Oh, dear, I must have signed with a not very good one, then.
(i didn't, as it happens.) when I had an offer in hand I took it to Zeno, John Jarrold, Juliet Mushens and a couple of others. These are all top, top agents - not one was interested in the offer in hand. (It was a fairly typical small publisher offer, no advance, royalties on net.)
An agent wants to seek the best possible financial outcome for you and the book. They'll put a lot of work into it. They want their fifteen percent to be of something decent. If you've subbed the manuscript all round you've cut that potential market for them to sub to. And publishers know the mss has been knocking around for a while, which makes it less attractive.
If you sub agents first and get nos, you have lost nothing except time - you can still take the book to publishers and, if you get a fab deal, go back to agents and ask if they'll consider you now (I did that with Zeno when I got the offer). If you've gone round publishers first and it puts an agent off - and it will, it gets asked on #askagent quite a lot and the responses are consistent - you have nowhere to go.
But, I'm not an industry expert. I am, though, someone who made that mistake with my first book and closed many, many doors before I got a chance to knock them.
if the article is a little dated, this may be the difference - it used to be much easier to get publisher offers than it is now, and there was a bigger market. That has shrank a lot and the agents have become more and more the gatekeepers to publishers. The consistent advice I see now, if you want an agent, is to get them first (with the query, synopsis route and any publishing credits you have) and then you work up to a publisher.