The simple answer is No. Your undamaged tires are not going to Blowout or Explode or Blowup if you see a pressure greater than xx psi on your TPMS or on your hand gauge.
There is a lot of confusion out there because people do not understand the reason for the confusing wording that is mandated by DOT.
There are Federal regulations on the words and information that must be molded on the tire sidewall. This wording has been around for years with some unchanged since the 1960's.
A recent poll of RV owners responding to a question on tire inflation number on the tire sidewall indicates that 18% think the inflation number molded on a tire sidewall number is the absolute highest a tire should ever have in it. Another 18% think that inflation is "the best" inflation for the tire 2% think it's the lowest pressure the tire should ever have. I am very disappointed with this level of confusion.
Here is the reality:
Each type and size tire and Load Range has a stated Maximum load it should ever be subjected to. The number is molded on the tire sidewall in both pounds and Kg. The tire industry has published tables that provide the MINIMUM inflation a given tire needs to support a stated load. The tables clearly state that the inflation number is the inflation measured before the tire is driven or warmed by direct sunlight. This is called "Cold Inflation". Not "Refrigerated" inflation and not some laboratory 68F or 70F "standard, but the inflation that would be the same as the surrounding ambient air. Some people know this as the "Temperature in the shade".
The confusion comes about because until recently vehicle owners never knew the operating temperature and pressure of their tires. However with the introduction of aftermarket TPMS as used by many RV owners, they now have those numbers presented to them.
What is missing are two things. One being training by the selling dealer as to what inflation is needed to support the stated load and second an explanation of what the words on the tire actually mean.
I am not sure if the RV salesman has ever received the training other than to tell the customer the information is in the Owner's Manual.
Hopefully when an RV owner reads "Max Load" they understand that they should never load the tire more than that.
The confusion comes with the inclusion of the word Max as it relates to tire pressure.
IMO the wording would be much better and more logical if the tire said "Max Load yyyy pounds at xx Psi cold".
I would leave it up to the people at DOT to try and explain why they were not consistent across all types of tires with the wording on load and inflation limits, but I have no idea who to ask. as I expect them to pass the question off and say "Ask the tire manufacturer" but the manufacturer is only following the regulations established by DOT.
I have a large number of posts in my blog that mention inflation. If you have questions I can suggest you review my posts as the questions are asked a few different ways and I provide the answer with what I believe is a consistent interpretation of the intent of the requirements.