As an engineer, I disagree. It's even possible Tom has the story slightly wrong too.
He is after all the songwriter, the artist, he is not the engineer.
When you are mixing and/or mastering you want the best possible coherency possible, you want to be able to put everything in the right place in a mix, you want the perfect balance when it comes to things like vocal reverbs and other effects, you want your imaging to be spot on.
You cannot do this on average speakers.
I would say they mix on the best studio monitors, then when they do their playback, they listen on the average/crappy speakers to reference what it will sound like in that situation, as well as listening on the proper monitors, and the near fields.
Then if they feel some changes can be made, they will do it on the proper studio monitors and then listen back on the average/crappy speakers.
I can tell you from experience, it is not possible to objectively mix on such speakers, it is pretty much like flying blind, you can't really hear what your doing properly, then when you do listen on some decent monitors, oh boy you are in for a wake up call.
It is very common practice to listen back on a few different types of speakers including consumer speakers, even consumer systems for that kind of reference, also listening back in mono to see how the mix sums as well. More common than you may think.