"The leader of that team then said the problem was as the alert was an email, they get too many of them etc"
IMHO that's one of the most critical things with any monitoring setup I've worked with, getting the dependencies setup correctly to reflect reality, and preventing those receiving the alerts from being flooded with alerts.
Eg if you have :
Firewall > Switch > HV Server > Virtual Server > various services on the server
all being monitored, where if something breaks and stops working then everything to the right of it will also be down, you only want to be alerted to the most critical item that's down on the left, otherwise for instance while you're scanning through the alerts for services on a VM that are showing as down, you can easily miss that the Firewall in front of it all has stopped responding. Off the back of that you need to have an understanding of how the infrastructure fits together, which services rely on each other etc.
At a basic level monitoring's simple, but once you start digging into it it can become a minefield.