"told by thier home inspector"
It appears that the HI is only partly aware of what he is saying. Sort of like the folks who can tell you E=MC2, but also believe in perpetual motion.
For the 'skinny' on this idea that you have to replace your fuses with breakers, one needs to look to the homeowners' insurance business. That industry has a few 'conventions' that need to be recognized.
The first is that ther are different levels, or 'forms,' of homeowners' insurance. These levels go from the 'best coverage and cheapest premiums' to the 'least coverage and highest premiums' types. Key to understanding this is that no company offers ALL the forms of homeowners' insurance.
One of the big 'turning points' is the age of the house. 40 years is the dividing line; at 40 years, coverage starts getting eliminated- UNLESS the home has been updated, remodeled, etc., to something resembling current codes. With the lesser 'forms,' the insurance company is also going to be looking at the details of the house a bit more closely, as well.
It's not so much 'does the house have fuses' as a question whether the house has been maintained, repaired, and worked on by competent people.
For our trade, well, the insurance companies look for the classic issues that lead to trouble. Here are different parts of the picture:
1) Service size .... 60 amps just isn't going to cut it with most folks these days- not with the multitude of appliances and central air conditioning. Insurance companies know that such homes usually have all manner of DIY electrical nightmares so that they could add air conditioning, dryers, etc. to the house;
2) Fuses .... Apart from the over-fusing issue, there's the simple matter of there not being enough circuits;
3) Lack of a ground wire with the branch circuits;
3) absence of receptacles in the bathroom, along the kitchen counter, or GFI protection anywhere; and,
4) Lack of an outside or main disconnecting means.
The short version is that a house with fuses will be difficult to insure- and that insurance will have a higher premium and greater restrictions than you might want.