Determining the size of the grounded (neutral) conductor isn't as easy as saying, hey let's take off 70% of the load and look that up on a chart.
I imagine the 70% that was spoken about refers to the allowable reduction of certain circuits named in NEC 220.61 (B)(1) which deals with cooking units and dryers. Those circuits, when the maximum unbalanced load is determined in accordance with 220.55 and 220.54 respectively, can be reduced by 70%.
But that doesn't equate to a total reduction of 70% because we're only speaking of a few of the circuits in the dwelling. Also, that doesn't include the 100% of circuits you can leave out do to the fact they are not supplied a grounded conductor and therefore, perhaps not obviously, do not contribute to the ampacity of the neutral anyway.
All in all, yes, you could have a total reduction of 70%, but I'd make the electrician prove it. For one, I wouldn't put the burden/responsibility on the homeowner to get my feeder cables - maybe a 250' spool of 14/2 romex but, at least by my experience, they'll screw that up too. So, I question that decision; I won't go as far as to call him names for it though.
If you did indeed have an actual 125 amp service or feeder rating you would need a #2 cu. or 1/0 al. or al. cu. (copper-clad aluminum) feeder according to TABLE 310.15(B)(7). Now, if you actually had a 70% allowable reduction you'd have...
125 * 0.70 = 87.5 A
...and according to TABLE 310.15(B)(16) you would need a #3 cu. or #2 al. or al. cu. cable.
Note that even this answer makes assumptions. You speak of a 125 amp service which doesn't equate to the actual minimum ampacity required, only the next largest standard breaker size. This leads to the fact that you may have an actual load less than 125 A. Taking 70% of the breaker size, if larger, would result in a larger reduction than is actually allowed.