OFDM transmitter oversampling

Hello,

I have a question regarding the OFDM transmitter. In order to reduce the
burden on the reconstruction filters, oversampling is used before feeding
the data to the DAC.

Oversampling, however, creates images of the baseband signal. To remove
these images, low pass filters are placed after the rate  up converter.
These filters are FIR systems, and, when applied to the signal, "smudge"
it in time domain, meaning that consecutive OFDM symbols are overlapping
each other before the data is even sent to the DAC.

In my understanding, this is exactly the problem created by the multipath
channel, and the cyclic prefix is added to make the linear convolution of
the signal with the channel impulse response analogous to a circular
convolution.

Why is it, then, that the convolution of the data with the interpolation
filter does not pose the same problem for the receiver as the multipath
channel?

Thanks.