Firstly, he used a Digitech Metal Master and Ibanez Tube Screamer played through a Marshall half stack

But what I'm wondering is does the amp you're using really matter that much if you're going to use the same pedals?

If you're playing through pedals the amp will be on the clean channel right? And you'll be concerned with only the EQ (bass/mid/treble) because the distortion comes from the pedal right?
Well, you're feeding certain frequencies into the amp, which also has its own character, so it may influence the pedal's tone.

If you want the pedal's tone ONLY, you'd probably play through a very plain-sounding amp, or even though the PA, but taht tends to sound bad.

That's why people like those tube amps with just one channel and a volume control: they're a blank canvas. They give you the tube warmth, but everything else comes from your guitar and pedals.

I've seen amps designed for pedals
The amp always adds its own tone to the mix but some more extreme distortion pedals can cover it up quite a bit but it still has an effect. some pedals will sound bad through some amps and good through others. oh and you dont have to use the clean channel all the time. that tube screamer would probably sound great through a dirty channel with the two distortions properly mixed together. i dont think you should have much trouble getting good sounds out of a marshall amp unless its solid state. ive said it a million times an amp thats not tube is like a guitar thats not wood. accept no substitutes.