Clogged Heater Core after Coolant Replacement

We've got a 2001 Ford Focus with around 80,000 miles on it. About a month ago we had the coolant replaced. Now we've noticed that the heater isn't working well. I took it back to the same repair shop, and they said that we have a partially clogged heater core.

I'm suspicious that the heater core started having problems so soon after the coolant was replaced, and I want to make sure that the repair shop didn't somehow cause the problem when they were doing other work. I read online that a clogged heater core can come from particles in the coolant.

Is it possible that the shop did a poor job with the coolant flush and caused a clog in the heater core, or is this just completely coincidence?