I can say with clarity that if old, not bold saw "a landrover stuck up to its axles in mud" on a designated stopway, then that stopway does not meet the requirements of ICAO Annex 14, and should not be used in the performance calculations whilst in that condition.
From a pavement engineering viewpoint, the stopway and RESA have to able to support a light vehicle (such as a landrover) without any rutting if they are to be strong enough not to cause major structural damage to an aircraft using them.
While each pavement needs its own testing and design, I can give rule-of-thumb guidance as to the sort of answer that you should get if you go asking questions (or that your airport inspector should be getting if they ask questions). And enough guidance to assess the validity of the answers, especially those given by shopkeepers and accountants.
The sort of numbers I’d be looking for as a minimum are pavement thickness of 150mm reasonable gravel (soaked CBR 45) on top of a sandy B subgrade (B being the ICAO strength rating). In the case of the airport where the landrover got stuck, I assume that the subgrade is a bit clayey and maybe a C rating, and so a pavement thickness of 125mm good gravel (CBR 45) on top of 125mm poor gravel (CBR 25) is the minimum. If it is a D rating, add another 100mm of poor gravel. And because of jet blast, wind and water erosion, the whole thing often needs to be surfaced with a light bituminous surfacing. If it is unsurfaced, add another 100mm of gravel to provide for the erosion. For the technocrats, I calculated this using the MePADs software based on the procedures used in the South African mechanistic – empirical design procedure, with design traffic from a US military spec, cross-checked by British Airways' unplanned research into bogging a B744 at Perth, and my own unplanned research into severe rutting and pavement damage using a 737-800 and a 767-200 of (I forget whom) at (I forget where).
If the stopway is in use, then the airport inspector of your country's regulator should be notified of the deviation from ICAO, and they can request that the airport produce evidence that the stopway complies. Standing above your regulator's head, and encouraging their genuine interest, is the new ICAO Safety Oversight Audit programme. When the audit occurs in your country, the auditors will be looking at pavement bearing strength and should require documented evidence of the regulatory requirements and effective compliance with these requirements. Don't forget to mention this to your regulator . . . . .