Not stupid at all.
What you need is a profile for the laser printer (and you should be calibrating and profiling the monitor, too, so you can trust what you see on screen). There may be a "canned" profile for the printer, but the odds that it's actually a good match for your particular printer are pretty slim.
The best thing is to buy an instument and software package to do the profiling yourself (the X-Rite Color Munki is relatively inexpensive and can do boththe monitor and the printers) so you can fine tune periodically, but there are services that will do a custom profile of your printer for less than $100 or so, and that may be good enough.
The printer in question, the Brother HL-4570CDW, is a fairly inexpensive SOHO laser printer typically used to print “office” documents. As such, it doesn't offer direct options either on the front panel or via the driver to match typical commercial print conditions such as SWOP. Most content sent to such a device is sent as RGB from printer drivers.
(For your convenience, I have attached a copy of both the specification sheet and the manual for this device!)
(1) Don't expect reasonable CMYK colors if you are using what Brother describes as the “Windows(r) printer driver (the most suitable printer driver for this product)” and what is apparently installed by default (see page 26 of manual). It invokes an emulation of HP PCL5C, pure RGB, which is a real problem from InDesign. Install their “BR-Script printer driver” and turn off the option for RGB vivid color and try that instead. BR-Script is Brother's emulation of PostScript 3 - definitely not Adobe PostScript 3, but it possibly will give you better results than their emulation of PCL5C!
(2) Assuming you are printing BR-Script and the colors are still very problematic, try recalibrating the printer via the printer's front panel. See page 82 of their manual!
(3) Export PDF as PDF/X-4 and try printing the PDF/X-4 file from Acrobat Pro or Adobe Reader, again using the BR-Script driver. This might improve things.
If you still can't get decent color and the printer is still “new,” I'd try to return the unit as defective. You can get much better printers for comparable prices from Xerox that have Adobe PostScript 3 and have reasonably good color. Otherwise, if still under warranty, I'd contact Brother and see if they have solutions other than blaming Adobe somehow!
PS: This isn't the first report I've heard of serious problems with Brother CloneScript devices.