You don't need dumbbells. I train at home a lot, and i don't use dumbbells.
You really don't miss out on much. True, barbell + dumbbell will trump simple barbell training, but it isn't required.
And Mumma, while starting strength is a solid book, it ain't the be all and end all of training. And work out 'everything'? ... well, I'm sure i can name some specialist isolation exercises that can not be done with a barbell (and if you could use one, you would be strong enough to not need a book). Also, some exercises are safer with a dumbbell, or at least more challenging with dumbbells.
As for 'David Betham', I'd buy a power rack over dumbbells any day. I don't understand how you're a pussy to use one - how do you get the bar to your back for back-squats? What if you want to remove the clean portion for front squats and overhead presses?
If you are referring to people who do crimes against weightlifting like curl in the rack, then yes, I'll agree.