You've lost me with that first line.
When looking at what a side has spent on their squad, you cannot look at transfer fees in isolation. Clubs spend far more in wages each season than they do on transfer fees after all. As I pointed out with the Ronaldo example, just because a transfer fee of a particular player might be less than another, the total package required to sign them may end up being far more. Thiago is another example. Most of the PL could afford the £25m fee but only 4 sides could have paid the wages to sign him.
Arsenal cannot compete financially with Liverpool, Chelsea, Utd or City, even if they did spend more on transfer fees last summer. And my figures were net. In terms of gross spend there's next to no difference between Liverpool and Arsenal over the past 5 years.