Is it safe to use a higher amperage rating fuse?

Today was my 2nd attempt at trying out Synergistic Research fuses.  About 3 years ago when I had separates, including mono block amps, I bought a set of Blue fuses.  One component had a mfg spec of 250mA and the retailer said go with 315mA.  My two mono block amps each had a 6.3A.  When I installed them one of them blew upon powering up.  The retailer said we should go up to the next rating.  I was a bit frustrated at the experience and didn't feel comfortable putting higher values in my expensive components.  I felt these expensive fuses should be made to tighter tolerances than the cheap BUSS fuses I had been using.  If I remember correctly, that was the actual argument that the dealer told me.  They are mfg to tighter tolerances so a 5A SR fuse was almost dead-on 5A while a cheap fuse may actually be 5.3A or whatever.  This also was a bit confusing at the time so I sent them all back.

Okay...3 years have passed and now I have a single integrated amp which has a 5A fuse.  Much less to invest in the upgrade so I ordered an Orange.  It came in today...installed....pressed power...on and off went the amp.  DAMN!!  I contacted the retailer and SR on the same email.  This was a different dealer from 3 years ago.  The retailer said I should go to the next value up.  I said no and and they are waiting for the tracking info of my return shipment.

I did a quick search of my question before posting and saw a thread about the Red fuses and someone said they had to do the exact same thing.  Is everyone putting higher rated fuses in their gear that is worth thousands of dollars?  Is there no risk in this?  I admit that I don't know what could actually happen from that.  It seems that other things could burn up if a higher amperage fuse is in place.  I am compelled to simply stick to the mfg specs for something that I don't understand because I don't want to create problems just from a simple tweak.

Should I let them ship me a 6.3A or just be done with this?