If you have a tubeless tire and you use Slime, or a product similar to slime, it is just about impossible for the tire shop to fix a flat in the tire after you have used Slime.
what problems have you seen with this?
most slime products are 100% water based, ( with suspended particles ), and can be washed out, and then have the tire casing cleaned around the patch area with solvent.
I'v applied inner- patches to tubeles tire casings on many occasions after a slime product was used to limp it for a couple years.
after washing the casing out with soap and water and then dried, I cleaned the patch area with a solvent like hexane or 3m adhesive and wax remover.. makes a nice surface for a patch. used regular flat / round farm and or 'bike' style patches ( red backed ) that you use the can of rubber cement to stick them on with, not the adhesive backed patches.. etc.
have yet to have a failure of one of those patches. ( fingers crossed / knocking on wood now )
sounds more like a lazy shop running that line on you, wanting to sell you a new tire or something...
On tires that have seen the sealer / inflators that use the sticky rubbery gun.. it's more of a pita to clean up.. sometimes leaves webbing and other stuff.. on those, I clean the spot to be patched withthe 3m product, and then glue the patch on.. those usually require bead sealer to be applied to get a good seal.. I us ethe big can of balkamp bead sealer. not to mention the rim needs to be buffed down and cleaned up.. etc. usually replace the valve stems in those as well as they tend to stick..
then again.. I do my own tire work too.. that may be the difference... the worker, not the actual materials or product itself.
soundguy