I would rather have people not talking about my team than talking about them because I lost significant talent in a "trade down in value" trade. You can always get them to talk about your team later on.
And as IP wisely stated, and he should know given he's been to like the last 3 or 4 straight Finals in this game, trading a 3 for three 1's is not equal value. Trading down 20 spots in the 1st, 2nd or 3rd round does not equal trading up two rounds from the 6th, 7th or 8th rounds. It just doesn't, especially around where the middle of talent tiers lay.
That's how I did my Big Board pre-draft when I was playing. I made tiers and then saw where the cut offs looked like they were going to fall and tried to work trades moving up in tiers, not rounds. There's a big difference when you do that.