Many RV owners do not understand the inflation and load information that is molded on the sidewall of the tires they own. As a tire design engineer, part of my responsibility was to specify all the words, symbols and numbers on the tire sidewalls. Some of the words such as brand name like as Goodyear or Michelin and the "line" like "Eagle" or "Transforce" are obviously selected by the sales and marketing departments.
The tire size or sizes had been selected and it was my job to design and request molds appropriate for the sizes that were to be part of the new line of tires. For each size, I needed to consult the US Tire & Rim Association data book and to specify the appropriate load and inflation numbers for the maximum allowable for the Load Range of each tire. With LT lines we might have LR-C, LR-D and LR-E tires and if incorrect numbers ended up on the tires they would need to be recalled and replaced for free so it was obvious that this information had to be correct.
With the exception of a few tires that are designed for a new model of a specific car or Light Truck from Ford, GM, Toyota, M-B etc, I would never know what vehicle the tires would end up being mounted on so there would be no way for me to specify a specific load or inflation for any given tire that was vehicle specific. Selecting the tire and Load Range and specifying the inflation number to be posted on the vehicle Certification label is, by regulation, the responsibility of the vehicle manufacturer. It was however my responsibility to ensure the tire was capable of passing the DOT tests as well as company minimums based on the use of industry standard loads and inflation numbers.
All tires have a Maximum Load capacity molded on the tire sidewall along with the minimum inflation needed to support that load.
With this background information I hope you now understand that the inflation number molded on the tire sidewall is not selected or made up by the tire engineer as the inflation number comes from the published Industry standards. The inflation on the Certification Label aka Tire Placard is specified by the RV manufacturer and by federal Regulation must be sufficient to support the GAWR (Gross Axle Weight Rating) which is part of the RV company design process.
The placard inflation may be equal or less than the number on the tire sidewall but it should never be higher than the tire sidewall pressure number.
Ideally you would have actual scale loads with the RV fully loaded at its expected heaviest. With that load known you can consult the tables to learn the minimum inflation needed to support your load. However if you don't have scale readings the best thing to do is inflate your tires to the placard information. This is OK as long as you have not overloaded your tires. Note that the tables for tires made by Goodyear are the same as for tires made by General, or Firestone, or Bridgestone, or Cooper. Also most Michelin tires have the same numbers as the other tire companies with the exception of a few tires that were originally designed for European country application where metric units are standard. When converting to the US "Inch-Pound" units the numbers do not always match up so if you have Michelin tires you probably need to consult their tables. You can also check the tables listed on this blog post.
If you review the above you will see that I am not advising that you use the inflation on the tire sidewall, unless that is the inflation on your Placard.
A side comment on the inflation number of the tire. The words may be "Max Inflation" on some tires, but this is related to the way loads are established for tires based on the inflation. The LIMIT is the stated maximum load. The intent in the wording is to stress that the tire load can not be increased even if the inflation is increased above the number associated with the tire's "Maximum Load".
Regarding hot tire inflation numbers higher than the number on the tire sidewall, that is OK as long as the set "cold inflation" is not set higher than the number on the tire. Tire inflation will increase when the tire temperature increases. The rate of change is about 2% for a change of 10F. Seeing your "Hot" inflation higher than the tire sidewall is not a big deal. With the advent of TPMS many people are seeing tire temperature or pressure increase for the first time as a driver. Most TPMS have the high temperature set to 158F. I have found that setting the high pressure to 125% of your cold set pressure should normally avoid having the alarm sound as long you are not overloading your tire or pushing your driving speed. If you get close you might just drop the speed back a few mph. Personally I set my cruse to 62 or 63 mph and stay in the right lane. I do not get people honking and I get real good fuel economy. (10.2 mpg in my last 1,200 mile trip from Ohio to WY).