Does that mean that all these wonderful low readings that I have been getting are totally invalid?
No.
There are two important points to understand:
central corneal thickness ("CCT") cannot be used to adjust IOP for any individual patient. It is used in research across populations and one can make some general statements for population averages. That's all. Your doctor cannot say that your IOP should be adjusted up or down because of your corneal thickness. If your doctor tells you that, they are making a mistake. Some people have thick but more flexible corneas; some people have thin but stiff corneas. CCT won't tell you how your corneal properties affect a tonometer like the Icare or Goldmann.
there is a population average effect that thicker corneas tend to cause the tonometer to overestimate IOP. You cannot know if that is happening in your individual case based on your CCT alone. (You could obtain a corneal biomechanical measurement with a Reichert Ocular Response Analyzer, to determine that, however.)
If you want to take a guess based on CCT, your tonometer may be overestimating your IOP, meaning your true IOP values could actually be lower. But I advise you not to make such a guess. CCT cannot be used for that purpose. See point #1 above. Unless your corneas are extreme, your Icare IOP will not need to be adjusted. Keep in mind that Goldmann tonometers are also affected the same way, yet ophthalmologists rely on the Goldmann tonometer every day.
The best advice I can offer you is to trust your Icare. The fact that you can take your IOP at home at all hours of the day or night and under many different life situations means that your own IOP data set will be far more complete and accurate than your ophthalmologist's IOP data records for you. Therefore, your Icare represents a vast improvement in your IOP data set. It is not perfect -- no tonometer is. But the best thing you can do is to trust your own IOP data. There is no better source of IOP data than the data you collect at home.
If you want to maximize the accuracy and completeness of your home IOP data, please see these answers:
In addition to that, you can find a doctor with a Reichert Ocular Response Analyzer (ORA). Dr. David Richardson has one, for example. Many ophthalmologists do. The ORA measurements will tell you whether a Goldmann (or Icare) will tend to overestimate or underestimate your IOP. This instrument can also give your a "CH" value will independently help predict your risk of glaucoma progression. That "CH" value is relatively stable. It does not change like IOP.
For more background on your initial question, please see these two answers:
Please do not create new tags when you ask questions. Use the existing tags. Also, please vote on the best answers and accept the answer (using the checkmark icon) that answers your question. Thanks.