"Atletico,Juventus and Dortmund have spent less than Arsenal and City and still did better in recent years"... by recent years you mean only the last 2 seasons? the comment you were replying to was talking about the english clubs hopefully dominating again after spending this summer - keyword - Dominate.
Atletico,Dortmund and Juventus have not been dominant in Europe, they have had 2 good seasons in the CL on average per team with 2 of those teams losing in the Final, Juve might make it 3 - not exactly domination is it? and Dortmund and Atletico seem to be regressing in both the CL and their various leagues as they are unable to spend, which suggests that you cannot maintain a level of consistency without spending well in the transfer window.
In regards to the comments about spending, The bloke alluded to the fact that English Clubs have been terrible in the the transfer window in recent years and they might make it right this summer, whilst i agree with your comment about spending not being the only factor, i think the likes of Barca,Real and Bayern have proven that all you need to do is spend and spend well in order to be consistent in Europe.