Yes sadly this is possible and it has already been done to Mixxx. If you want some examples see the programs: TinyDJ (tiny dj dot net), Digital DJ Pro (music-oasis dot com slash download slash Audio slash Digital-DJ-Pro), and DJ Mixer Studio (djmixerstudio dot com). I won't link to them here so they do not get any link-credit from mixxx.org and please do not Google for them either.
These are just clones of Mixxx, re-branded. This is possible due to Mixxx's open-source license (the GPLv2). Open-source is about sharing and re-using code so this is one possible use of the Mixxx codebase. In each of these cases, due to the requirements of the GPLv2 these re-branded versions of Mixxx must also provide the source code for all of their modifications to Mixxx. We have been in contact with these companies to make sure that they do follow the requirements of the GPL.
Contrary to popular belief it is totally legal to sell open-source software (even under the GPL). If you sell it, you must provide the source code along with the software also licensed under the GPL. The buyer of the software has every right to turn around and offer the source to that software to the world for free since she received that source code under the GPL. This means that selling open-source software is hard to make profitable. The most common thing you'll see is an eBay seller selling a "SuperDJ" software that is just Mixxx rebranded. An unsuspecting eBayer might buy this for $1 and never know that it's actually Mixxx. This business model relies on the buyer not knowing any better.
If someone were to violate our copyright -- to take our code and distribute a modified version of it without releasing their modifications under the GPL, then we would have a valid copyright violation complaint against that person/business. The GPL-violations project
is an organization of pro-bono lawyers who pursue GPL violators so it is not unheard of for GPL violators to be brought to justice.
There is a separate issue of trademark. If someone were to distribute Mixxx without re-branding it then they would be violating our trademark and we could go after them that way. In the past, we asked distributors of re-branded versions of Mixxx to remove our trademarked materials (e.g. skins, logos, etc.) from their re-distributed version of Mixxx. There is precedent for this -- see "firefox vs. iceweasel".
Finally, to address your point of not being able to tell if a piece of software contains code from the Mixxx project -- there are various forensic tests you can do. We have done symbol analysis of various major DJ software (e.g. VirtualDJ) and have been able to detect from the symbols they left in their binaries that they have stolen code from open-source projects such as FFMPEG without attribution or following license requirements. Beyond this you can do more advanced things to test if the code of a program was taken from another. In the case of wholesale clones of Mixxx it is painfully obvious to a Mixxx developer. There are so many quirks that are specific to Mixxx that would allow you to uniquely tell that it was Mixxx under the hood even if the developer had gone to great lengths to conceal it.
Hope this helps,