Kevin- you are absolutely correct.
Many brands use coring below the waterline. Cruisers Yachts, Inc., Sea Ray, etc. Coring is not a bad thing in and of itself- typically the problem comes from an owner down the road deciding to make adjustments, add a thru hull or something of that nature and they don't seal things properly and then you have water getting to the core. With synthetic that is not a good situation but it is not catastrophic. A balsa cored hull though....now that can be a problem.
Solid fiberglass is not necessarily the answer either. LOTS of solid glass hulls have lots of blister problems in a big way. I've got a good friend right now with his 50' Taiwanese built trawler on the hard right now due to dinner plate sized blisters. Or you can have hatteras which will blister like clockwork but they are so solid it's not really an issue.
When it comes to older boats though it is hard to say one method is better than the other. Brand and to a certain extent, construction methods, become not as important as how well the vessel has been cared for over the years. I can show you solid glass hulled boats that are absolute train wrecks due to neglect and I can show you cored hull boats and even balsa cored hull boats that are very old and the boats are wonderful in wonderful shape. Most boaters (ok, not trawler folk but boaters in general) "love" sea rays yet how many of the 1990's model sea rays have water logged stringers? Of note too is that while lots of trawlers may have solid glass hulls, they often also have wood stringers wrapped in fiberglass which are very much capable of rotting from within.
My Monk 36 had a fair # of very small blisters when we bought her and began the refit yet my bayliner 45 that had not been hauled out in about 4 years didn't have a single blister on her at all this spring when we hauled her out for repair and refit and new bottom paint.
Saying all the above I'd still probably suggest that it's best to minimize one's probability of having issues so choose your individual boat wisely- not just on brand and construction method- but actual condition, upgrades, and evidence of long term maintenance. Would I want a balsa cored hull- not me personally. Synthetic core- acceptable for me personally.