Yes, you are correct!
At least there is a physiological explanation.
The construction of the human hearing apparatus causes a quality that is called critical bands.
A critical band represents a bandwidth in which a sounding frequency has to be alone for us to hear or perceive it clearly.
This bandwidth is, relatively speaking, increasingly wider for lower frequencies (less than 1000 Hz) and thus close notes are more likely to be perceived as dissonant in low musical registers.
If two tone frequencies are close to each other they disturb overlapping regions of the basilar membrane - where the hair cells are located - within the cochlea in the inner ear; but if the frequencies are far apart they stimulate two separate regions. The range of frequencies, in relation to a base frequency, that have a stimuli overlap is called the critical band for that base frequency.
If two tones are close enough - within approximately 10 Hz - they are fused and perceived as one tone with a beating, i.e modulation of the amplitude. (Unless they have the exact same frequency which will only generate a louder single tone.)
Increasing the frequency difference of the two tones to more than 10 Hz, but still with overlapping critical bands you pretty much hear one tone but with an unpleasant roughness (constituted by very fast beating).
When approaching a separation of the two tones' critical bands they will be perceived as two separate tones.
For frequencies above cirka 1000 Hz the critical bandwidth (in Hz) is a fixed fraction of roughly 15% of the frequency, so for higher octaves there shouldn't be a physiological difference in the perception of dissonance for the same tones.
But for frequencies below this the critical bandwidth is constant at about 100 Hz. This means that the critical band of a musical scale tone will encompass more and more surrounding notes as the frequencies get low and the frequency differences become small. That is; an interval (or chord) that was quite consonant in a high register might become dissonant in a low register because the tones' critical bands overlap there.
The highest amount of roughness or dissonance is perceived when the frequency difference is about 30% of the appropriate critical bandwidth. Which means about 30 Hz apart for tones below 1000 Hz.
Further, all of this applies to all overtone partials of a tone from a musical instrument.
Lets look at an example with frequencies (in Hz) for C and D and their first set of overtone partials. First the C and D one octave below middle-C:
Note 1st 2nd 3rd 4th 5th 6th
C3 130.8 261.6 391.4 523.3 654.1 784.9
D3 146.8 293.7 440.5 587.3 734.2 881.0
The first partials are 16 Hz apart which is within the critical band and yet more than 10 Hz apart, and thus will be perceived with roughness; i.e. as dissonance. The second partials are about 30 Hz apart, which here is 30% of the critical bandwidth and will therefor be perceived as rather much dissonant. The higher partials up to the sixth have increasing frequency differences, and since the critical bandwidth here is still (almost) constant they have decreasing roughness (with frequency differences representing about 50% to 80% of the critical bandwidth.) Also the higher partials are likely weaker for the tone on the instrument and therefor have a smaller impact on the dissonace perception.
Now let's look at the frequencies of the C and D one octave above middle-C:
Note 1st 2nd 3rd 4th 5th 6th
C5 523.3 1047 1570 2093 2616 3140
D5 587.3 1175 1762 2349 2937 3524
The frequency difference of the first partials is at about 64% of the critical bandwidth. For the rest of the partials it's at about 82% of the critical bandwidth. This causes roughness or dissonance but not nearly as much as frequency differences at the roughness peak at 30% of the critical bandwidth such as was present in the C3-D3 chord.
Therefor the C3-D3 is perceived as more dissonant than the C5-D5!
I suppose different individuals might have different critical bands distribution over their hearing range, and of course the perception of dissonance is subjective (and cultural), but this is a general physiological explanation of why hauptstadt and others perceives greater dissonance for the same interval in lower registers than in high.
1. Musical Acoustics s.e, by Donald E. Hall, Brooks/Cole Publishing
I hope I got this right. It was a long time since I studied these kind of things.