" ... so the engineering is certainly there ... "

That is a howler.
There is a reason that these mega-companies have multiple brands. I don't think it is to give the consumers the best product at a bargain price by changing the wrapper. If you want cheap just go with Harder Fart (TM) products. Use it until it fails. Rinse, Lather, Repeat.
I hear your conspiracy, but Bosch is a bit different. They don't sponsor me and I've never taken a dime or a free tool from them.
I have, however, been to one of their events before and it's a super interesting company. About 92% of Bosch's shares are owned by a non-profit that was set up by Robert Bosch's family. The remaining 8% is owned by the family.
Most of the profits earned throughout the year go back into Bosch... But dividends that are paid out go mostly (92% actually) to charitable/humanitarian causes. When I was getting my MBA at OU, I did a paper on the company and became obsessed with how they run the joint.
Two things fascinated me:
1. It's one of the largest private companies in the world... And it's ran not for the health of any one person, but for the health of the company itself and longevity. Lots of strange and unique policies within.
2. They spend more on R&D than just about any competing company in the space and yet, they aren't head and shoulders above any of them. I've always wanted to see a break down of that... but, of course, it's private.
Anyway, Bosch has different brands to attack different markets. So, I'd bet Dremel was acquired to hit a lower price point. For instance, they design a multi-tool for professionals and give it the Bosch brand. They then take that same basic design, cut some corners, lower the price and give it the Dremel brand.
From what I know about Bosch, I'd be shocked if there was anything nefarious going on as far as marketing, branding, etc...
But then again, there is that whole Bosch/VW emission thing...