Oh great, another vinyl vs. the world debate.
Yes, in theory analog media have perfect reproduction. In real life this does not happen for a number of reasons the most important of which is that the medium (in this case vinyl) has very real physical limitations. For one thing, you have a limited dynamic range because of the way the media is both recorded and read. Since there is a needle that has to follow the groove you can only make the groove "wiggle" so much before the needle can't follow properly and you get distortion. Now, a laser turntable would be better, but when they're recording they're assuming that most people have mechanical turntables not optical ones so they have to limit the dynamic range. Secondly your record is vulnerable to all kinds of environmental issues. If the room gets warm, cold, moist, etc. you are directly affecting the medium and by consequence the sound since it's an analog medium. Next, because of the way the record is both written and read, you have to live with relatively large tracks that mean a large record. It also makes it impractical for any portable uses as was mentionned abve.
Moving on to CDs then. These are definitely not perfect either, nonetheless they have the practical advantage that the data stored is much more robust than on vinyl. Yes the both the ADC and the DAC add some amount of noise to the signal, this is inevitable. What is more important however is that the quality of both the ADC (at the recording end) and the DAC in your CD can be implemented in different ways that have different compromises. Depending on the amount of effort that you put into the reconstruction of the signal the quantization noise caused by the conversion can be reduced. On top of this, you have to remember that there are analog components to your CD player or amplifier since sooner or later you have to convert the signal back to analog and do some power amplification before you send it out to your speakers. The way you handle each step and the quality of every component plays a factor in the final sound quality. Obviously, you can't expect a $30 cheapo CD player to sound as good as a $400 turntable.
With all this said, the CD format is very good but not without it's imperfections. In most cases, people prefer vinyl not because it's more accurate, but because the they *like* the distortions caused during the playback (eg the "warm sound" of vinyl). Nonetheless, if you look at a format like DVD-A, it's such ridiculous overkill compared to what the ear can perceive that these arguments are pretty much moot.
To put things in perspective, it is generally agreed that the human ear can perceive sounds up to 20 KHz, hence Sony and Philips originally used a 44.1 KHz sampling rate specification for the CD. DVD-Audio, on the other hand allows for sampling rates of up to 192 KHz which means that you can faithfully reproduce sounds of about approximately 96 KHz. Now, without going into the details of filter design, this makes it easier to have a flat passband for the relatively low frequency audible sound. Next, DVD-A allows for words to be up to 24 bits long; a 24-bit DAC would give you a noise floor of about -144dB. Meaning that the softest sound is about 16 million times softer than the louest sound. In practical terms, with a noise floor that low, the quantization noise isn't what's limiting your sound quality.
So, long story short the people who claim that analog is better than digital are only right in theory.