over can be used in this context, but in my (UK English) opinion it is, as you suggest, misleading. The Oxford and Cambridge dictionaries have a definition of over as above, which would mean above the maximum value of the range. Merriam Webster also suggests that it can also mean within a range:
(1): all through or throughout
- showed me over the house
- went over his notes
(2): used as a function word connecting one mathematical set and another whose > elements are coefficients or values of parameters used to form elements of the > first set
- polynomials over the field of real numbers
Meaning 1 suggests a very systematic coverage of the range: this doesn't fit with can be in your sentence. Meaning 2 is a bit technical.
Looking at actual usages, this NGram graph shows that adjusted within the range is marginally more popular, and the majority of usages of adjusted over the range are from technical documents, for example:
... an Atomika ion source and electronically processed into pulses 10-500 ns long by two sets of electrostatic deflection plates and four apertures (which can be adjusted over the range 0.125-4 mm diameter). Ferroelectric thin films
The number of usages is quite small, but it seems to me that over is somewhat more widely used with this meaning in US English than in UK english. This opinion is supported by the inclusion of a relevant definition in Merriam-Webster but not in the Oxford or Cambridge dictionaries.