I wrote about this quite some time ago, based on personal experience. I've been writing about it on this forum ever since.
If you're taking doses that are as far different as the ones you take, your INR will (other factors considered) fluctuate based on the day when you test. It's preferable, if possible, to vary your daily doses as little as possible from day to day, so that when you DO go to the clinic, their reading will more likely reflect an actual INR (and not one that changes from day to day).
Warfarin is really pretty cheap -- locally, it's about ten bucks for 90 pills. With a combination of dosages, and your willingness to break a pill in half if necessary, you can come pretty close to the same dosage each day -- or alternate with a dose that's only one mg (or is it mcg?) above or below other days. With minimal fluctuation, your INR should be roughly the same from day to day.
Back when I had a supply of strips (I'm down to three -- does anyone have any expired InRatio strips that they may be willing to sell or give away?), I was able to test on different days - not compulsively testing daily - but sometimes 8 days apart, sometimes less -- and I had a time when I had an INR of 1.4, and I tested fairly frequently to see if my dosing adjustments were effective (and not overly so). I saw that there can be fluctuations based on dosages a particular day (though I didn't try to figure WHICH day a particular INR related to, nor did I make wholesale changes in dosing).
All I'm suggesting is that your clinic is probably not exactly correct with its conclusion -- you should try testing on varying days of the week, just to see if your INR fluctuates based on the day you test. (And as Superman said, if the variance in your INR, probably related to varying dosage, is still within range, you should be okay. It's only when your INR is at high or low ends of the range and your clinic starts tweaking your dosage, that you may wind up with problems staying in range again.)