I don't agree with this. I've explained it on other threads but am happy to recap.
It isn't necessarily a bidding war on who has more money. It has to do with the money teams are able to allocate to a position and how much they are WILLING to allocate.
For example...let's say the Rams view Saffold as a $5M/year player...but only have $4M/year to allocate to that position. However, the Chiefs also view Saffold as a $5M/year player and DO have the money to allocate to that player. Now the cap number has climbed and both teams are able allocate the $5M/year to Saffold...it doesn't necessarily mean that the Chiefs are going to outbid the Rams and throw $6M/year.
I don't think Rodger Saffold is viewed at such high esteem that teams are going to be highly bidding for his services. I think he will get some very fair offers from numerous teams, and very well could be more than the Rams are willing to pay...but I think the salary cap raise only helps the Rams and only possibly stays neutral.