It does impinge on traceability. I actually do this with grocery stores to fuck with their data mining -- I don't have one of those discount cards for any of the local places I shop at. I do, however, have several friends' phone numbers memorized, and I use those to identify "myself" for the discounts. My friends are aware of this, and find it hilarious. Especially the non-smokers who now get ads for tobacco in their mailboxes. 
That actually works out to their advantage, depending on the grocery store chain. My local chain Kroger/Frys has deals with Shell gas stations such that if you buy $XX worth of groceries, you get $.10 off per gallon of gas you buy.