Interestingly, a recent paper draft from the Icahn School of Medicine at Mount Sinai supports Trump's claim as far NYC is concerned. It could have been a matter of luck as to which strain actually spread (the most) in NYC, but there were apparently a more introduction events from Europe, so basically more "coin flips" in that basket until one turned lucky.
isolate had documented exposure through travel to the Middle East (clade A3) and the second
through travel to Europe (clade B). Neither of these showed evidence of onward transmission, so
we therefore excluded these two cases from any inference made from the phylogenetic analyses.
For the remaining isolates, the great majority (87%) cluster with clade A2a. This clade is largely
composed of isolates obtained from patients with COVID19 in Europe (72%; Figure 2B),
suggesting that introductions from Europe account for the majority of cases found in NYC in the first weeks of March 2020.
[...] The earliest sequences at the base of
clade A2a include isolates from Italy, Finland, Spain, France, the UK, and other European
countries from late February, in addition to a few North American isolates (Canada and US) from
the first week of March 2020. [...]
For the rest of the clades (B, B1, and B4), we identified four putative SARS-CoV-2 virus
introductions to NYC as early as February 20 (90%CI: January 29 to February 26) (Table 1).
Notably, two of these introductions were inferred to be of domestic origin based on their close relationship with US isolates, including those from the main community transmission in Washington state (Clade B1) (Bedford et al. 2020). The introduction of this clade to the East Coast
was recently reported (Fauver et al. 2020). Although more than half of the sequences in clade B
were of Asian origin (Figure 2B) the closest relatives to the NY isolates were of European and
North American origin. The isolate that belongs to clade B4 is positioned in a cluster with two US
sequences from WA state, with an inferred date of introduction to NY in early March (Table 1)
and a prior period of untracked transmission in unknown location(s) since January 21 2020 (90%
CI: January 18 to January 23). Prior to this period, the closest viral isolates basal to this cluster
are from Australia and China (Figure S1). [...]
Taken together, our results show that the NYC SARS-CoV-2 epidemic has been mainly sourced
from untracked transmission between the US and Europe, with limited evidence of direct
introductions from China where the virus originated.
So yeah, the strain that spread the most in NYC apparently came mostly directly from Europe, but it was preceded e.g. by one from the Middle East. Why that other one didn't spread is of course hard to peg to a concrete event like luck or something else (e.g. effective quarantine) since the paper doesn't detail such matters.
Also, a smaller fraction of the NYC cases was traced (domestically) to Washington state and from there to China/Australia.
They also note some limitations of their study, mainly in terms of sampling
A limitation of our analysis is the relatively small number of isolates from cases identified in the
first week of March 2020 which means that our model relies on inferences based on sequences
deposited in the GISAID database. Since sequencing efforts vary by country, the fraction of
sequences available by region/country is not necessarily representative of the number of cases
reported for each of these regions. Thus, some of these inferences may change as more complete
and representative SARS-CoV-2 sequences become available.
Also, one can quibble that NYC is a "single cluster", but I think the ISMMS paper is still interesting enough in its findings in terms of (which) strain(s) spread in NYC.