Sure it's possible. Just because water/detergent is flowing through doesn't mean much of it is. It takes a high amount of pressure to clear out channels which are clogged if water is still able to flow through other routes.
(Before you continue reading all of this though read through the diagnostics posted at the end... might save you a lot of time)
Are you guys using any cleaning/detergent/acid products such as Prestone to clean the system? More caustic solutions will work far more quickly than plain water or citric acid based detergents (Prestone) but need to be thoroughly neutralized after flushing (a final flush with a baking soda solution is all). I've heard from a couple radiator specialists that phosphoric acid is not to be used. Oxalic acid is more effective than citric but less aggressive than muriatic (hydrochloric) acid. Although, I generally don't think it's a good idea to use very caustic cleansers (such as muriatic acid) in a system where a clog may allow the acid to sit in a pocket and keep munching away at good metal... They're excellent for once a year or two year scrubbing of healthy systems. You could try it but be forewarned that if there are any weak spots (a collection of rust particles holding hands) you may finally compromise them. There are solutions available with inhibitors to slow the acid from consuming the good alloys, I recommend you find one and follow the directions closely. As with any coolant cleanser (including the citric acid based ones) it takes time for scale and rust to be dissolved and cleared out... You'll just add it and run it for anything from one day up to a week. Don't expect instant results.
When flushing old systems, flush it until it runs clear; Then, give it another pass with detergent and flush until clear again. Do this until it's pretty much clear right away. In a heavily scaled, blocked and rust filled system this may take quite a while depending on the detergents used and the period they're required to be in the system. Also this wouldn't be a bad time to add a coolant filter, you're going to be freeing up a LOT of shit and it's also just a good thing to have installed. Back flush when flushing on each pass, any large particulate that is freed up is a potential blockage.
If you have the equipment (a 15 to 20psi manometer and a pressure gauge) I'd recommend testing the pressure drop across the heater core. I suspect that a healthy heater core shouldn't see a drop of more than a couple psi but clogged will see a drop of 33% or more... I'm not certain on those figures but that's what I would look for.
Two other things to check are:
http://www.cygnusx1.net/Supra/Librar...aspx?S=AC&P=43
http://www.cygnusx1.net/Supra/Librar...aspx?S=AC&P=37
The air mixture valve in the dash will not open unless the thermistor reports the coolant in the heater core as up to temp.
I hope this helps, it's not exactly my area of expertise.