Not sure what he means by not using water the night of regeneration. Not many users will ever know WHEN their softener regenerates, and since the standard programming has it going at 0200, it should be moxnix, unless you are coming home from the club and showering during a regen. In which case, you'd be using untreated water in the event of a single tank system (not a big deal once a week or so), or perhaps exceeding the SFR on a dual-tank system.
And the wear to which F6Hawk refers (and it's not a fear, it's a fact) is simply being pointed out that a system that regens every night will in fact wear out 10 times faster than one that regens every 10 days (assuming "industry standard" parts, and that nothing is defective to cause premature failure).
Your numbers are correct, 69,120 in 7 days, covered by a 3.5 cu ft using 6 lbs of salt. You will use about 1095 lbs of salt, and cost yerself about $110 annually (assuming $4.10 per 40# bag).
Or you could drop down to a 3.0 cu ft, save about $350 on the softener, program it for 24 lbs of salt, spend about $15 more per year... it would take you 23 years before you started seeing a gain in $$$ on the 3.5 cu ft system (assuming average online prices).