What does it mean to over sample?
As you sequence a library you are sampling from the pool of all possible oligonucleotides found in it. This is a stochastic process, meaning that you are more likely to sequence a piece of DNA that is more prevalent. 

As you increase the number of reads that you sequence for a library, you decrease the chances of seeing a new read that you have not yet seen before. If you plot the number of unique reads per total reads sequenced, it will look something like the cumulative density function of the exponential distribution, where you have diminishing returns on unique sequences as you continue to sequence.

If you sequence a library and quickly stop seeing unique reads, we say that this library has low complexity. Therefore, you have "oversampled" it if you sequence too deeply. I am guessing that your metagenomics library actually has a lot fewer species/unique sequences than they anticipated, and that you sequenced deeply anticipating more.

Edit: In response to your comments, the bigger problem in 16S analyses is not sequencing too deeply, it is over-amplifying your samples such that they no longer represent what is actually in your gut microbiome samples. In this case if you used read normalization you would not accurately represent what was in the library that you sequenced since the amplified molecules (16S) are so small that you only have len(16S molecule)-(read len) + 1 possible reads in each direction. You might consider removing PCR duplicates with GATK but this will still have the same effect of not representing what was in the sequencing pool. It is very possible that you have many PCR duplicates after 16S amplification. I generally don't trust amplicon sequencing for quantitive analyses, and don't really trust for low coverage "is-this-species-there-or-not" either, especially when dealing with the 'dark matter' of uncharacterized species. You might be well off just asking "is this species present in high coverage at this time point?"