IMO this reccomendation in your department makes a lot of sense.
If you have a group in your department where they only publish papers in a specialized journal, it makes it that much more difficult to assess the quality of their research. The good thing about having a central core of competitive journals (like the Annals, Inventiones, Advances, JAMS, etc) is that you have a vetting place for ideas across fields.
To put it to extremes, if there's a group in your department that publishes in only one journal, and all the people that publish in that journal only publish in that journal, this leads to suspicion that the journal publishes pretty much anything (at least for that group of people).
Trying to publish in general journals, that's a first step towards getting some percentage of papers in that field into broader circulation. This is what we need if we want to be a community and not simply warring factions.