I'd consider those instructions as fairly detrimental. The primary bud will always have the biggest flower. The secondary buds will always have smaller flowers or may not flower at all, regardless of the TLC bestowed. I think the potential is predetermined by the quantity of starches stored during the previous growing season and by the structure of the embryonic bud, also set during the previous growing season.

The only time I pinch buds on my peonies is when they send up a stalk with 3 buds. I always snip out the center bud to make room for the other two to flower. It also 'lightens the load' during a rainfall, and keeps the plant from drooping so badly.

I've never heard of pinching back buds. I have a young 3 year old peony which came up with a huge number of flowers this 3rd year. Thank goodness because I got this plant on those end of season type sales. it looked like it was dying.. so I took pity on it. Now it rewards me with a terrific spray of flowers. I also purchased a brand new peony as a root earlier this year. To my surprise it actually gave me a bud this year - and it's beautiful. I am looking foward to it's next show.
ianna