I know for one particular popular area south of Playa, that's VERY true and a real disgrace. An NGO in an area south of Playa likes to talk about nets and training they've gotten for some of their staff and local DMs from a Nature Conservancy grant, but everyone I know who's dived or snorkeled in the same town as the NGO in the last few months has similar reports - they are seeing the lionfish, pointing them out to the DM and/or going to the NGO office to report, and nobody seems to be interested in catching them. Two people recently told me that a DM's response was that it's not his job. Another said he's getting more tips when people see lionfish, and since the reefs in that area aren't so great these days, he's fine with something interesting and exotic to keep people coming.
I actually commented to the NGO that maybe they should send some of the local DMs over to Cozumel for a few days. The dive shops in Coz can tell them why they need to get on board with capturing or killing the lionfish and show them how it's done. I don't get it. These people just don't seem to understand that if they do nothing, what marine life they do have on their reefs will get wiped out, the reef will decline even further and then their services won't be needed. Nobody comes to snorkel or dive a dead reef!
