You may be at a constant pressure altitude but will be descending relative to the ground. Keep the same 'power' setting, add a bit of Isaac Newton and .....
You are quite close, actually.
This was the theory behind pressure pattern navigation used many years ago on long range trans-oceanic flights.
These aircraft were normally equipped with a hi-range radio altimeter, which was used to find the true height, and thereby remain in a least headwind/greater tailwind situation, even though the actual ground track may be more nautical miles...the desired outcome was a minimum
time track.
Now, on to position errors....and slightly faster airplanes.
With the original B707, rather large pitot/static errors were noted, so much so that the raw data info could not be reliably used.
Enter KIFIS...Kollsman Intregrated Flight Instrument System, an early sort of air data 'computer', that took in the raw pilot/static inputs, ran it through a series of 'corrections' and out came improved reliable instrument indications.
Usually.
Then, enter the combined pitot/static probe.
This provided reduced position errors, and its use on some of the first generation wide-body jets (L1011, B747), combined with a true ADC system, provided very accurate airspeed/pressure altitude information.
For light GA aircraft, look for (sometimes) pronounced static errors due in large part to the location of static ports....in relation to the pitot probe.