The answer to your question is definitely no on 2 accounts.
First, what you call "less" depends on the purposes of your analysis (more on that in a sec). Second, a hotter air can hold more water before saturation, not the contrary.
Absolute humidity (AH) is defined as the mass of water per unit volume of air.
Relative humidity (RH) is defined as the ratio of the current AH, to the saturation AH (which is the maximum absolute humidity the air can hold before it starts to condensate into droplets).
The saturation humidity increases with temperature. So, in a sense, you are right (if we invert your claim) in saying that at same RH but higher temperature, your AH will be higher (since $AH=RH*AH_{sat}(T)$). In this case, the warmer air will hold more mass of water per volume.
However, in a meteorolgical context, it would likely not be pertinent to point that up. The relevant quantity here is indeed RH.
To illustrate, let's say it's hot outside. You're cooling yourself off by evaporating sweat off your skin. The rate at which you can evaporate it and thus chill will be limited by the humidity already present in the air, more precisely by the relative humidity. Since RH is a measure of how close you are to saturation, it is the one that is significant in telling you how much your evaporation rate will be lowered.
In short, when it comes to measuring human comfort in a meteorolgical condition, AH would be misleading while RH is pertinent IMO. I believe people are not committing a misconception, but instead using the appropriate tool when referring to RH to compare two climatic conditions.