This actually makes a lot of sense to me. I haven't experimented with this, but I wouldn't be surprised if it didn't turn out to be true.
I'll have to try this out myself, because I desperately want to hold on to my current companion.
My suspicions were aroused when Lydia, who was the veritable bulwark for my ricepaper-like caster, started to become more and more fragile as I levelled up -- eventually I started tanking for
her! After I made the switch to Eola, I started to figure that perhaps since you can pick Lydia up so early, she's mean to be somewhat weaker as companions go. Lately though, Eola has started to fall behind as well, and I also thought it very suspicious that she hasn't started using any Expert-level spells (she and I were both up to Adept when I recruited her), whereas Illia (whom I only recruited recently) most definitely is.
On the other hand, I also became kinda suspicious about the 'stat raising while away' phenomena when I dropped in on Brylana (sp) of the College (whom I recruited not too long after I first recruited Lydia), and had her join the you-know-whos. After she became a member, I observed her going a few rounds with 'D,' and was surprised that she could... well, go a few rounds with 'D,' when by all rights she should have been eviscerated in short order.
As for Lydia, she has been putting the 'house' back in 'housecarl' at Breezehome for many game days now, so I'll check in on her and see if she's regained any of her former glory. Fingers crossed, because barring a fix in 1.2 or some future patch, this would be the only potential fix for console users who, ironically, don't have access to the console to fix such things. I'll report back here with the results, and would encourage others to do the same. It would be especially helpful if it turns out to be true at all, if the span of days necessary to reset the companion was recorded.
EDIT: Ok, well I tried it out and I'd have to rule it as 'inconclusive.' Lydia definitely hadn't improved: she could barely take out a Restless Draugr (and I'm @ level 38, for reference), and a Snow Troll ends her in 1-2 hits. I tried waiting 8+ days before collecting my other follower, Eola, and there did seem to be some improvement there... but finding a place to test before-and-after Eola so that she'd be up against exactly the same odds was very difficult.
I think that this is something for the PC guys to try, as they can actually access the stats themselves instead of having to infer them.