I want to know about Chex Systems dings and their affect on current bank accounts?

I have a ding on my Chex Systems report for NSF and overdrafts at Wells Fargo. This account was sent to collections and I need to make payments... However, they are asking for payments way out of my "payable" range... so I can't do the full amount they are asking me for. They told me that I should get it paid off soon or else my current bank (Chase) could run a Chex Systems report and find that ding and proceed to put a hold on the funds in my account with them... is this true or is the collections agency just fear mongering?