It’s more that it’s easier for bacteria to collect in one place and become ‘dense’ enough in a particular location to become a problem in stagnant water.
Just for the sake of this argument let’s pretend that you’ve got a collection of water on either side of you, one that’s just a sitting puddle, and one that’s a gently flowing stream. And at the same time you toss in a clump of bacteria into each one, and that each clump will reproduce and make a million new bacteria every minute, regardless of which water collection it’s in.
On the stagnant puddle side, as each minute goes by, there’s a million more bacteria, and they just keep “piling up” until the puddle can’t support anymore.
But on the flowing side, many of those bacteria are being swept away, and there’s a constant supply of clean water coming in and diluting what’s left.
A flowing water source isn’t really infinite, but it’s a lot more water than a completely static amount of water, so it’s going to be a lot harder to saturate with bacteria.
Latest Answers