Sure there might be some disagreements around the nature of the inflation measure (e.g. it doesn't include house prices) but that's another discussion.
Edit: It's worth noting that money supply is believed to be mostly endogenous these days. The monetary system we currently have is a credit based system in that all money is someone's liability and the supply of this money is mostly based upon the demand for credit. The system is quite complicated. The FED uses short term interest rates to influence the demand for credit. Low rates rates make credit creation more likely (stimulates demand). Whereas high rates decrease the amount of credit creation (curtails demand). Furthermore, if people pay back loans then we experience deflation. If there is not enough credit then we experience deflation. If there is too much credit, we get inflation. Here I'm assuming that the credit is spent. I.e. velocity increases. Indeed, people don't borrow and leave the money in their accounts. Instead, they use it to make purchases! General inflation or inflation in a particular market becomes particularly acute if credit is not allocated appropriately. For example during the housing bubble which popped in 2008. The issue here was underwriting standards were not fit for purpose.