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?
It seems like a very poor business strategy.  Most, I would say 99.9% of the people would want to replace a fuse in their gear with a matching rating.  This is what any MFG is going to recommend as they should.  

It simply doesn't make sense to me.  I can be very cynical but I don't think the entire industry is a scam where they are simply taking cheap fuses and painting them or whatever.  I believe there is engineering, R&D, etc. involved, but I don't understand why their fuses cannot handle current the way a 'stock' fuse can.  This should be priority #1 in designing a fuse.

I DO NOT believe that all 'stock' fuses have incorrect specs and are allowing different values of current than they are claiming.  I believe the mistake lies with these high end fuses.  So if that is the case, why don't they correct this where people don't have to send back blown fuses and then try plan B with a higher value fuse.  This has left me without confidence in their product.  

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You can use a small value capacitor, 0.01 uF and smaller wired between live and ground to mitigate the noise.
Note, if you wire the capacitor upstream from the fuse, you have to use a capacitor that is rated to be used on mains I.e. a class Y capacitor.

Downstream from the fuse you can use a regular film capacitor.

If you connect a capacitor from line or neutral to AC ground, anywhere on the AC side, no matter before or after the fuse, use a Y rated safety capacitor. Where it is in relationship to the fuse does not matter. One of these small capacitors failing will not take out the fuse, it will just increase the leakage current to ground to a dangerous level. 

No need to replace a fuse at all even in a power amplifier. A well designed power supply is a buffer to anything happening before it including the fuse. Yes, the fuse limits current into the power supply (exactly the idea) but the audio circuits do not see that. In other words this idea of designer fuses is just another attack on lay instinct in order to extract money from you. If you really are concerned just wire by the fuse. Your house's circuit breakers should prevent the fire but, if something goes south be ready to replace the piece. I use to do this with power amplifiers but have stopped as it does absolutely nothing to improve sound quality. I proved that to myself with AB testing after an electrical engineer friend told me I was being silly. He was right.  
Even the Littellfuse audiophile fuses are over priced at $50.00/5. But, at least you can be sure they will meet spec. I see no reason to spend that kind of money on something sonically insignificant.
Yes, the fuse limits current into the power supply (exactly the idea) but the audio circuits do not see that

Correct because the big "musical transient" amperage that’s needed, does not come from the fuse, it comes from the reserves of "powersupply storage caps".
The mains fuse side is a just a "trickle charger" (for an analogy) to top up those power supply caps, if they (the caps) run out of storage while playing music then **** hits the fan.
And if the fuse is higher rated then your equipment is in big trouble

Cheers George