The cosmology of the Speed Force is always changing based on the era, writer, context, and accordingly its mechanics.
Grant Morrison's work-around is that basically all worlds are a part of the "DC Universe" and just about all of the rational realms (tangible, scientific, material, and real... vs. magical, spiritual, metaphysical) were surrounded and governed by the Speed Force. You can see a pictorial illustration of this principle in the infamous Map of the Multiverse:
During Mark Waid's era- the inventor of the Speed Force in fiction- the Force was an extra-dimensional energy used to justify everything Speedsters did. When he first developed the concept, the idea was that Flashes were like batteries and could and would eventually become pure energy beings... inspired by the idea that Barry would become the very bolt of lightning that began his career through Crisis.
This energy being concept became the idea of carrying the Speed Force in and with them where (and when) ever they went, since they literally WERE the Speed Force. Waid predicted this for Wally down the road:
Then had Wally become this during normal continuity, until his romantic "lightning rod", Linda Park, brought him back to his senses and corporeal self. From that point on, Waid started to use romantic logic, quasi-mystical lens to interpret the Speed Force such that it was basically akin to THE Force from Star Wars ilk.
This conception has had the longest run with various writers having various takes on it. In some cross-overs, the Speed Force is inaccessible in other dimensions... but in other takes (like when Bart Allen briefly took over the role of The Flash) it was again something that could be bottled up and carried in a particular Flash never to be parted with.
Finally, Geoff Johns innovated on the Speed Force with a nonsensical word-salad of technobabble explaining how Barry Allen is and will forever be the source of the Speed Force, generating it by using it.
The goal was primarily rhetoric to justify Barry's return and Wally's demotion, but it also served to suggest Flash is inseparable from the Speed Force. Which, incidentally, aligns nicely with Barry's cameo in the Marvel Universe as "Buried Alien" wherein he still had his speed and trounced all-comers in a cosmic race.
In sum, your friend has an argument that Flash can be separated from the Speed Force- and thus his powers- based on the venue of the race; but there are many counter-examples to the contrary allowing Flash to maintain his speed across universes and continuities, which use a different reasoning for access-to or carrying-of the power (be it always accessible, or carried within, or becoming it, or generating it). Given the variety of treatments, no one interpretation should be dispositive.