If it's up to Capcom, then I can't think of a single reason why it wouldn't also release on PS4. Lets face it though, it's probably not Capcom's decision to make as much as it is Nintendo's at this point.
Marketing deal with Nintendo. That, and they don't want to split the market. If you have part of yourself customers on one ecosystem and another part in other, then a lot of the appeal of MH is lost.
I can totally see Sony reaching Capcom for this game, PS4's sales in Japan have been less than stellar, although healthy, and the sudden release of the Switch make that console much less appealing.
If PS4 becomes irrelevant in Japan, and I mean by that, selling 5k or so every week instead of 15k, then a lot of smaller games will switch (TM) from that console, and believe it or not, those titles are extremely important for a console's success, because they bridge the gap between big releases, and it would have Sony competing with MS without Japanese games, competing in MS's turf.
I can also see Capcom signing the deal, seduced by the prospect of growing the series popularity in the west.
The panicking part is also logical, I don't think anyone could have predicted the Switch's popularity worldwide (not even Nintendo, seeing they are not even close to meet demand), looking in retrospect it's a really stupid decision that may hurt the franchise as a whole.
Making two games (MH5 and MHP5) is double the cost, and the fanboy wars it will spawn will hurt the franchise. The marketing deal with Nintendo probably changed for the worse for Capcom. MH5 vs real MH, here we go!
Seeing how the SFV deal hurt that franchise (stupidly so IMO, never understood that decision), I fully understand the panicking part.
I believe the rumour, only because Capcom gonna Capcom. No bread, no crumbs.