2004 F150 cam phasers

I just bought a 2004 F150 4x4 with the 5.4 Triton.
Before I bought it all the cam phasers , sprockets,
timing chains, guides, and oil pump were replaced.
I put less than 150 miles on it and I changed the oil
I went with synthetic and didn't use a fram oil filter
(lol). Used motor craft. When I was done with the
oil change with in a couple of seconds the service
engine light soon light came on and it threw 4
codes saying bank 1&2  were retarded and the
timing was backed off. I noticed that the top of the
vct module on the passenger side was kinds dirty
so I unplugged it took it out to clean it and the part
that was inside of the engine looked brand new I
used electrical cleaner and cleaned the connection
real good then did the drivers side as well. It was
really dirty put everything back together when I
started the truck everything seemed fine just had
the slight tick let it run for about 10 min reved it a
couple of times and the service engine light never
came on. So I took it for a drive and about 15
min.as I was coming to a stop  at a light it started
idling rough but when I gave it gas it drove smooth.
No miss no hesitation, ran like it should . The next
2 lights that i stopped at  it idled smooth like
normal but the next light it was rough again . But
the  service engine light soon hadn't come on . I
took it to a shop to have them look at it to find out
what the problem was and they said the cam
phasers and timing chains, guides etc... we're  bad
and needed to be changed . Said that oil pressure
was causing the problem. Now I can't see how
changing the oil could make Brad new parts go
bad . Doesn't make sence. And if oil pressure is an
issue can a higher flow/out put oil pump be used ?
Don't know if they even make such a thing . But if
there is one that is made can it be used with out
causing other problems due to the higher oil
pressure?