Resampling, oversampling and ASRC (Asynchronous Sample Rate Conversion) are three different things.
Oversampling is done natively inside nearly all DACs. It is a necessary step for a proper digital-to-analog conversion, especially at 44100 Hz. Some exotic high-end designs are capable of converting to analog without any oversampling (the "NOS" ones). This is a mistake, coming from a complete misunderstanding of the basic science of digital PCM. They believe that oversampling is "something" on the path of the signal and that it is better to "remove" it.
It is the same thing as saying that the crossover of a 2-way speaker is something in the path of the signal and that it should be removed.
Resampling is changing the sample rate of the digital data before sending it to the DAC. It occurs in computers, or devices that need to mix together several tracks before sending them to a DAC. They convert everything to, say, 48 kHz, then they sum each sample to mix the tracks together, then they play the resulting 48 kHz stream. In many cases, they keep converting to 48 kHz even when they just playback a single 44.1 kHz track. It is possible to do this nearly without quality loss, but not all devices do this well.
Last, ASRC is a sample rate conversion whose rate can vary in realtime. It allows to mix two S/Pdif streams together, for example. Since both streams have their own clock, they slowly drift from one another. ASRC resamples them to another independant clock. It is extremely difficult to do it without quality loss, because the speed must be adjusted by extremely small increments, and converting from, say 44099 Hz to 44100 Hz produces a lot of aliasing.
In computers, the VLC video player has built-in ASRC. As such, the speed can change audibly during playback. Turning off ASRC while playing local files is a feature that has been asked for years to the VLC team (it is only needed to playback realtime streaming, such as radio stations), but no one has volunteered yet to do the job. It was also used in the Reclock filter, that allowed to play back DVD in computers following the video clock instead of the audio clock, to avoid micro-judder in the picture. This one could adjust the speed more precisely than VLC, but in counterpart, it introduced clearly audible aliasing in the sound (the triangle of the orchestra in 2001 space odyssey made "tiwiwiwink" instead of "tinnnnnk").
ASRC must be avoided in high fidelity. It may be used in "anti-jitter" devices. These little boxes pretend to eliminate the jitter that comes from a CD Drive feeding an external DAC. This is nonsense. First, DACs eliminate all the jitter from their digital input. All that's left in the analog output comes from the DAC itself. Second, there is no reason for the drive to have more jitter than the anti-jitter device itself. Third, if the device uses ASRC (some may just use PLLs), it harms the sound quality much more than any amount of jitter could.