Gombrich is not even a Buddhist. Buddhists are advised to take refuge in the Noble Sangha rather than in non-Buddhists. If what you posted is really true, then Gombrich is clearly mistaken.
The ‘beliefs’ or 'views" I was referring to are listed in MN 117 therefore it may not include every idea that happened to find its way into the EBTs.
‘Re-birth’ is not a ‘belief’. It is a knowable reality. That wholesome actions lead to a ‘happy’ or ‘heavenly’ state & unwholesome actions lead to a ‘hellish’ or state of ‘deprivation’ is a reality rather than a belief. If you optionally chose to extend this reality to after the termination of life, you can. But if you exclude this reality from the current life, I personally say you are very mistaken.
The problem with the physical interpretation of the follow verse is it excludes the operation of kammic results in the current life.
When my concentrated mind was thus purified, bright, unblemished, rid of imperfection, malleable, wieldy, steady, and attained to imperturbability, I directed it to knowledge of the passing away and reappearance of beings. With the divine eye, which is purified and surpasses the human, I saw beings passing away and reappearing, inferior and superior, fair and ugly, fortunate and unfortunate. I understood how beings pass on according to their actions thus: ‘These worthy beings who were ill conducted in body, speech, and mind, revilers of noble ones, wrong in their views, giving effect to wrong view in their actions, on the dissolution of the body, after death, have reappeared in a state of deprivation, in a bad destination, in perdition, even in hell; but these worthy beings who were well conducted in body, speech, and mind, not revilers of noble ones, right in their views, giving effect to right view in their actions, on the dissolution of the body, after death, have reappeared in a good destination, even in the heavenly world.’ Thus with the divine eye, which is purified and surpasses the human, I saw beings passing away and reappearing, inferior and superior, fair and ugly, fortunate and unfortunate, and I understood how beings pass on according to their actions. MN 4
As I previously posted, the words ‘birth’ (‘jati’) & ‘death’ (‘marana’) appear to not always be ‘physical’ in the EBTs. If Gombrich does not discern this, then he must not be a very good scholar.
For example, the two verses below, if interpreted ‘physically’, state the arahant does not die but the non-arahant dies, which is the opposite of the general idea Buddhists have about ‘re-birth’.
Heedfulness is the path to the Deathless. Heedlessness is the path to death. The heedful die not. The heedless are as if dead already. Dhp21
Bhikkhu, ‘I am’ is a conceiving; ‘I am this’ is a conceiving; ‘I shall be’ is a conceiving; ‘I shall not be’ is a conceiving; ‘I shall be possessed of form’ is a conceiving; ‘I shall be formless’ is a conceiving; ‘I shall be percipient’ is a conceiving; ‘I shall be non-percipient’ is a conceiving; ‘I shall be neither-percipient-nor-non-percipient’ is a conceiving. Conceiving is a disease, conceiving is a tumour, conceiving is a dart. By overcoming all conceivings, bhikkhu, one is called a sage at peace. And the sage at peace is not born, does not age, does not die; he is not shaken and does not yearn. For there is nothing present in him by which he might be born. Not being born, how could he age? Not ageing, how could he die? Not dying, how could he be shaken? Not being shaken, why should he yearn? MN 140