It's probably easier to say that managers aren't the only factor, rather than insinuate that in many circumstances they're irrelevant. People would stomach that, because well, it's true. Obviously some managers have greater effect than others, some managers are good managers in the wrong environment, some shit managers buy their way to stability/success. That's the point though, there's a shit load of variables.
Does money help? Course it does, but it's not the be all and end all. The top sides that spend big, sustain success or are at the very least, more likely to, but teams at the top end also falter due to the manager - look at the inconsistencies of City, or Chelsea without Mourinho. Arsenal aren't the highest spender, but like us they've spent enough to challenge, yet have consistently failed to do so over the last decade.