That sounds exactly like the sending fax is document is stalling, so a single line across the page gets sent for a few seconds. You can easily check your own machine's scan and print quality by putting anything in the doc feeder and copying it.
To test the print section alone, use the menus (or I think your model has a separate Report button) to print out the Help list.
It's possible that both your sending correspondents have slick, hard document feeder rollers, but you'd think they would have heard complaints from others. I can't think of anything at your end that would stretch out your prints, and there's no Bulletin about it on Brother's service website.
On the off chance you have a glitch in your machine's memory fouling it up, you can clear it out. This page
has instructions for clearing out only the image memory (91) or all of it (01). It may or may not help, but only takes a couple of minutes to try.