When my home was inspected, the inspector said something about this being incorrect, but I can't remember what he said I should do.
Well,
home inspectors are generalists who don't know every bit of Code.
That said, you should look at what is actually on the report, rather than leaving us to guess.
I realize your relationship with the inspector was following him around and listening, but that isn't worth the paper it's printed on. The report is what matters.
The breakers are with in sight of the units and can be locked off. I think the issue was that it shouldn't be a 60 amp breaker, that it should be a smaller breaker at the main breaker box.
Being in sight and within 50' of the units negates the requirement to lock them off.
If he is saying something about breaker size, that may be due to the size of the wire.
#8 copper NM or UF cable is only good for 40A.
#8 copper anything-else cable is only good for 50A.
#8 aluminum, forget it.
#6 copper NM or UF cable is only good for 55A.
#6 anything else is good for 65A.
#6 aluminum is good for 55A.
#4 anything is good enough.
So... if your wire is good for
less than 60A, it's not the end of the world -- but you will need to do a load calculation to see if the air conditioner units can fit inside that ampacity. The fact that the A/C breakers are 30A does not need that the 2 units need 60A. Some of that 30A is for design margin to reduce nuisance trips. That's why a load calculation is needed to see if these loads will fit on the wire you have.
So rule 1: Wire >= load.
-----
As far as breakers... once the above is ascertained, and you are sure the wire is large enough for the load, you need to
choose a breaker to fit the wire. Same rule here, Breaker <= Wire, except with an asterisk: if the particular breaker size isn't offered, you can
round up to the next available breaker.
So rule 2: Breaker <= wire EXCEPT rounding UP allowed.
Example: Your load calculation for both units works out to 51A. 55A wire is acceptable since 51<55. You can round up to 60A breaker because 55A breakers are not offered.
Example: Your load calculation comes out to 58A. 55A wire
is not big enough period fullstop. No rounding up allowed. Wire must be replaced.
Example: Your load calculation comes out to 39A. You already have #6Cu UF (55A). You are allowed to breaker at 55A since the wire is good for that. Therefore you are allowed to round up to 60A breaker since 55A is not made.