I think there's a possibility that the results are accurate...due to the way 23andMe performs their computations. I would expect quite different numbers if both kits were uploaded to GEDmatch and compared there.
At 23andMe, where there is at least one shared segment, they count the total, combined length of all the half-identical regions. This is what the other companies do; but since a portion of the child's genome is expected to be fully-identical, where there are two shared segments at the same location, 23andMe extends that and double-counts that fully-identical segment. Also, 23andMe adds any X-chromosome matching segment(s) into the total, which the other companies, and GEDmatch, don't do.
For comparison, FTDNA considers each gamete as contributing about 3400cM of material, for a total of about 6800cM; autosomal, no X counted. GEDmatch uses the same basic assumption, to the best of my knowledge. At 23andMe, though--and with the X included--a female genome is considered to be 7439cM, and a male's 7257cM...the difference there being the X-chromosome. The 4,416.7cM amount still seems high, but I can't speak to way 23andMe actually presents the raw data. If you're totaling using something like MS Access or Excel, we may be double-adding some values, like the fully-identical segments in the autosomes.
If uploaded to GEDmatch, I'd think the match should be more in-line with what you'd normally be expecting. I can't say with certainty this is the case, but if they're willing to create GEDmatch accounts it will be a quick way to check.